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Call number: | 9783319393391:ONLINE Show nearby items on shelf |
Title: | Singularities in Geometry, Topology, Foliations and Dynamics A Celebration of the 60th Birthday of José Seade, Merida, Mexico, December 2014 |
Author(s): | |
Date: | 2017 |
Size: | 1 online resource (XVII, 231 p. 15 illus., 10 illus. in color p.) |
Contents: | Extending the action of Schottky groups on the complex anti-de Sitter space to the projective space -- Puiseux Parametric Equations via the Amoeba of the Discriminant -- Some open questions on arithmetic Zariski pairs -- Logarithmic |
vector fields and the Severi strata in the discriminant -- Classification of Isolated Polar Weighted Homogeneous Singularities -- Rational and iterated maps, degeneracy loci, and the generalized Riemann-Hurwitz formula -- On singular | |
varieties with smooth subvarieties -- On Polars of Plane Branches -- Singular Intersections of Quadrics I -- A New Conjecture, a New Invariant, and a New Non-splitting Result -- Lipschitz geometry does not determine embedded | |
topological type -- Projective transverse structures for some foliations -- Chern classes and transversality for singular spaces | |
ISBN: | 9783319393391 |
Series: | eBooks |
Series: | Springer eBooks |
Series: | Springer 2017 package |
Keywords: | Mathematics , Algebraic geometry , Global analysis (Mathematics) , Manifolds (Mathematics) , Functions of complex variables , Mathematics , Several Complex Variables and Analytic Spaces , Algebraic Geometry , Global Analysis and Analysis on Manifolds |
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Call number: | SPRINGER-2016-9789462391710:ONLINE Show nearby items on shelf |
Title: | Noether's Theorems Applications in Mechanics and Field Theory |
Author(s): |
Gennadi Sardanashvily |
Date: | 2016 |
Edition: | 1st ed. 2016 |
Size: | 1 online resource (297 p.) |
Note: | 10.2991/978-94-6239-171-0 |
Contents: | Calculus of variations on ﬁbre bundles -- Noether’s ﬁrst theorem -- Lagrangian and Hamiltonian ﬁeld theories -- Lagrangian and Hamiltonian nonrelativistic mechanics -- Global Kepler problem -- Calculus of variations on graded bundles -- Noe ther’s second theorems -- Yang–Mills gauge theory on principal bundles -- SUSY gauge theory on principal graded bundles -- Gauge gravitation theory on natural bundles -- Chern–Simons topological ﬁeld theory -- Topological BF theory |
ISBN: | 9789462391710 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Atlantis Studies in Variational Geometry: 3 |
Keywords: | Mathematics , Global analysis (Mathematics) , Manifolds (Mathematics) , Mathematical physics , Mechanics , Mathematics , Global Analysis and Analysis on Manifolds , Mechanics , Mathematical Applications in the Physical Sciences |
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Call number: | SPRINGER-2016-9783658106331:ONLINE Show nearby items on shelf |
Title: | Manifolds, Sheaves, and Cohomology |
Author(s): |
Torsten Wedhorn |
Date: | 2016 |
Size: | 1 online resource (354 p.) |
Note: | 10.1007/978-3-658-10633-1 |
Contents: | Topological Preliminaries -- Algebraic Topological Preliminaries -- Sheaves -- Manifolds -- Local Theory of Manifolds -- Lie Groups -- Torsors and Non-abelian Cech Cohomology -- Bundles -- Soft Sheaves -- Cohomology of Complexes of Sheaves -- Cohom ology of Sheaves of Locally Constant Functions -- Appendix: Basic Topology, The Language of Categories, Basic Algebra, Homological Algebra, Local Analysis |
ISBN: | 9783658106331 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Category theory (Mathematics) , Homological algebra , Topological groups , Lie groups , Global analysis (Mathematics) , Manifolds (Mathematics) , Differential geometry , Mathematics , Category Theory, Homological Algebra , Topological Groups, Lie Groups , Differential Geometry , Global Analysis and Analysis on Manifolds |
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Call number: | SPRINGER-2016-9783319317564:ONLINE Show nearby items on shelf |
Title: | Geometric Methods in Physics XXXIV Workshop, Białowieża, Poland, June 28 – July 4, 2015 |
Author(s): | |
Date: | 2016 |
Size: | 1 online resource (20 p.) |
Note: | 10.1007/978-3-319-31756-4 |
ISBN: | 9783319317564 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Group theory , Global analysis (Mathematics) , Manifolds (Mathematics) , Physics , Mathematics , Group Theory and Generalizations , Global Analysis and Analysis on Manifolds , Mathematical Methods in Physics |
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Call number: | SPRINGER-2016-9783319313382:ONLINE Show nearby items on shelf |
Title: | Essays in Mathematics and its Applications In Honor of Vladimir Arnold |
Author(s): | |
Date: | 2016 |
Size: | 1 online resource (22 p.) |
Note: | 10.1007/978-3-319-31338-2 |
Contents: | A new way to compute the Rodrigues coefficients of functions of the Lie groups of matrices (D. Andrica, O.L. Chender) -- Quasimodes in integrable systems and semi-classical limit (M. Baldo, F. Raciti) -- Manifolds which are complex and symplectic bu t not Kahler (G. Bazzoni, V. Munoz) -- Solvability of a non clamped frictional contact problem with adhesion (O. Chau, D. Goeleven, R. Oujja) -- The Kolmogorov-Arnold-Moser (KAM) and Nekhoroshev Theorems with Arbitrary Time Dependence (A. Fortunati, S. Wi ggins) -- Iterative Methods for the Elastography Inverse Problem of Locating Tumors (B. Jadamba, A.A. Khan, F. Raciti, C. Tammer, B. Winkler) -- Transversality theory with applications to differential equations (D. Motreanu, V.V. Motreanu) -- Lattice-like subsets of Euclidean Jordan algebras (A.B. Nemeth, S.Z. Nemeth) -- Simultaneous Diophantine approximation: Searching for analogues of Hurwitz’ theorem (W.G. Nowak) -- On the fixed points of a Hamiltonian diffeomorphism in presence of |
fundamental group (K. Ono, A. Pajitnov) -- Some Generalizations of Fixed Point Theorems on S-Metric Spaces (N.Y. Ozgur, N.A. Tas) -- Functional Inequalities in Banach Spaces and Fuzzy Banach Spaces (C. Park, J.R. Lee, T.M. Rassias) -- The Maslov Ind ex in PDEs Geometry (A. Prastaro) -- On the infimum of certain functionals (B. Ricceri) -- The Algebra of Gyrogroups: Cayley Theorem, Lagrange Theorem, and Isomorphism Theorems (T. Suksumran) -- Mild continuity properties of relations and relators in rela tor spaces (A. Szaz, A. Zakaria) -- Contraction Maps in Pseudometric Structures (M. Turinici) -- Novel Tools to Determine Hyperbolic Triangle Centers (A.A. Ungar) | |
ISBN: | 9783319313382 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Dynamics , Ergodic theory , Global analysis (Mathematics) , Manifolds (Mathematics) , Algebraic topology , Complex manifolds , Mathematics , Dynamical Systems and Ergodic Theory , Algebraic Topology , Manifolds and Cell Complexes (incl. Diff.Topology) , Global Analysis and Analysis on Manifolds |
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Call number: | SPRINGER-2016-9783319312811:ONLINE Show nearby items on shelf |
Title: | Mathematical Analysis, Approximation Theory and Their Applications |
Author(s): | |
Date: | 2016 |
Size: | 1 online resource (20 p.) |
Note: | 10.1007/978-3-319-31281-1 |
Contents: | A brief history of the Favard operator and its variants -- Bivariate extension of linear positive operators -- Positive Green’s Functions for Boundary Value Problems with Conformable Derivatives -- The retraction-displacement condition in the theo ry of fixed point equation with a convergent iterative algorithm -- An adaptive finite element method for solving a free boundary problem with periodic boundary conditions in lubrication theory -- Evolution solutions of equilibrium problems - a computatio nal approach -- Cantor, Banach and Baire theorems in generalized metric spaces -- A Survey of Perturbed Ostrowski Type Inequalities -- Hyers-Ulam-Rassias stability of the generalized Wilson’s functional equation -- Approximation under Exponential Growth Conditions by Szász and Baskakov Type Operators in the Complex Plane -- On the asymptotic behavior of sequences of positive linear approximation operators -- Approximation of functions by additive and by quadratic mappings -- Bernstein Type |
Inequalities concerning Growth of Polynomials -- Approximation for generalization of Baskakov-Durrmeyer operators -- A Tour on p (x)-Laplacian Problems When p = ∞ -- An umbral calculus approach to Bernoulli-Padé polynomials -- Hadamard Matrices: Insights into their growth factor and determinant computations -- Localized summability kernels for Jacobi expansions -- Quadrature rules with multiple nodes -- A -summability of sequences of linear conservative operators -- Simultaneous Weighted Approxim ation with Multivariate Baskakov-Schurer Operators -- Approximation of Discontinuous Functions by q-Bernstein Polynomials -- Nests, and their Role in the Orderability Problem -- Resolvent Operators for Some Classes of Integro-Differential Equations -- Com ponent Matrices of a Square Matrix and their Properties -- Solutions of Some Types of Differential Equations and of Their Associated Physical Problems by Means of Inverse Differential Operators -- A modified pointwise estimate on simultaneous | |
approximation by Bernstein polynomials -- Structural Fixed Point Results in Metric Spaces -- Models of Fuzzy Linear Regression: An Application in Engineering -- Properties of Functions of generalized bounded variations | |
ISBN: | 9783319312811 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Springer Optimization and Its Applications: 111 |
Keywords: | Mathematics , Global analysis (Mathematics) , Manifolds (Mathematics) , Operator theory , Special functions , Computer mathematics , Calculus of variations , Mathematics , Calculus of Variations and Optimal Control Optimization , Operator Theory , Special Functions , Global Analysis and Analysis on Manifolds , Computational Mathematics and Numerical Analysis |
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Call number: | SPRINGER-2016-9783319291161:ONLINE Show nearby items on shelf |
Title: | Noncommutative Analysis, Operator Theory and Applications |
Author(s): | |
Date: | 2016 |
Size: | 1 online resource (2 p.) |
Note: | 10.1007/978-3-319-29116-1 |
Contents: | Preface -- Pimsner algebras and noncommutative circle bundles -- A fractional Dirac operator -- On the Sylvester equation over quaternions -- The Essential Centre of the mod a Diagonalization Ideal Commutant of an n-tuple of Commuting Hermitian Ope rators -- Clifford-Hermite polynomials in fractional Clifford analysis -- Negative definite functions on groups with polynomial growth -- An introduction to superoscillatory sequences -- Restriction and factorization for isometric and symmetric operators in almost Pontryagin spaces -- Measurements vs Interactions: tracks in a Wilson cloud chamber -- The radii problems for holomorphic mappings in J∗-algebras -- Lévy Processes on Quantum Permutation Groups -- New results on old spectral triples for fract als -- Why are Orlicz spaces useful for Statistical Physics? |
ISBN: | 9783319291161 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Operator Theory: Advances and Applications: 252 |
Keywords: | Mathematics , Functional analysis , Global analysis (Mathematics) , Manifolds (Mathematics) , Operator theory , Mathematics , Functional Analysis , Operator Theory , Global Analysis and Analysis on Manifolds |
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Call number: | SPRINGER-2016-9783319281865:ONLINE Show nearby items on shelf |
Title: | Convexity and Discrete Geometry Including Graph Theory Mulhouse, France, September 2014 |
Author(s): | |
Date: | 2016 |
Size: | 1 online resource (39 p.) |
Note: | 10.1007/978-3-319-28186-5 |
Contents: | Introduction -- PART I Research Articles. Marcus: Tudor Zamfirescu: from convex to magic -- Yuan: Acute Triangulations of Rectangles, with Angles Bounded Below -- Skupien: Multi-compositions in exponential counting of hypohamiltonian snarks -- Shabb ir & T. Zamfirescu: Hamiltonicity in k-tree-Halin graphs -- Schneider: Reflections of planar convex bodies -- Rouyer: Steinhaus conditions for convex polyhedra -- Riviere: About the Hausdorff dimension of the set of endpoints of convex surfaces -- Prunesc u: About a surprising computer program of Matthias Müller -- Oliveros, Martinez & Montejano: Extremal results on intersection graphs of boxes in R^d -- Massé, Euler & Lemarchand: On the connected spanning cubic subgraph problem -- Kincses: On the Helly dimension of Hanner polytopes -- Itoh & Ohtsuka: Classification of normal 2-polyhedra of positive constant curvature -- Heppes & Jeronimo-Castro: T(4) families ofϕ-disjoint ovals -- Fruchard & Magazinov: Fair partitioning by straight lines -- |
Filip & Petrusel: Fixed point theorems for multivalued Zamfrescu operators in convex Kasahara spaces -- Et-Taoui: Complex conference matrices, complex Hadamard matrices and complex equiangular tight frames -- Chevallier, Fruchard & Vilcu: Envelopes of α-sections -- Bokowski & al.: Selected open and solved problems in computational synthetic geometry -- Bau: Reductions of 3-connected quadrangulations of the sphere -- Barany & Por: Paths on the sphere without small angles -- PART II Open Problem Note s. Zamfirescu T.: Two problems on cages for discs -- Zamfirescu Carol T.: Seven problems on hypohamiltonian and almost hypohamiltonian graphs -- Vilcu & Zamfirescu: Six problems on the length of the cut locus -- Simoes-Pereira: Existence Problems for Matr oidal Families -- Funar: Cubical Pachner moves -- Eckhoff: Problems in Discrete Geometry -- Chevallier & Fruchard: What is the minimal cardinal of a family which shatters all d-subsets of a finite set? -- Baskoro: Some open problems of Ramsey | |
minimal graphs. | |
ISBN: | 9783319281865 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Springer Proceedings in Mathematics & Statistics: 148 |
Keywords: | Mathematics , Global analysis (Mathematics) , Manifolds (Mathematics) , Convex geometry , Discrete geometry , Combinatorics , Graph theory , Mathematics , Convex and Discrete Geometry , Graph Theory , Combinatorics , Global Analysis and Analysis on Manifolds |
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Call number: | SPRINGER-2016-9783319243375:ONLINE Show nearby items on shelf |
Title: | Maximum Principles and Geometric Applications |
Author(s): |
Luis J Alías |
Date: | 2016 |
Edition: | 1st ed. 2016 |
Size: | 1 online resource (570 p.) |
Note: | 10.1007/978-3-319-24337-5 |
Contents: | A crash course in Riemannian geometry -- The Omori-Yau maximum principle -- New forms of the maximum principle -- Sufficient conditions for the validity of the weak maximum principle -- Miscellany results for submanifolds -- Applications to hypersu rfaces -- Hypersurfaces in warped products -- Applications to Ricci Solitons -- Spacelike hypersurfaces in Lorentzian spacetimes |
ISBN: | 9783319243375 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Global analysis (Mathematics) , Manifolds (Mathematics) , Partial differential equations , Geometry , Mathematics , Global Analysis and Analysis on Manifolds , Partial Differential Equations , Geometry |
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Call number: | SPRINGER-2016-9783319224077:ONLINE Show nearby items on shelf |
Title: | Quantization, PDEs, and Geometry The Interplay of Analysis and Mathematical Physics |
Author(s): | |
Date: | 2016 |
Edition: | 1st ed. 2016 |
Size: | 1 online resource (11 p.) |
Note: | 10.1007/978-3-319-22407-7 |
Contents: | Introduction -- Todor Gramchev: Gelfand-Shilov Spaces: Structural Properties and Applications to Pseudodifferential Operators in \R^n -- Miroslav Englis: An Excursion into Berezin-Toeplitz Quantization and Related Topics -- Andrew Comech: Global At traction to Solitary Waves -- Irina Markina: Geodesics in Geometry with Constraints and Applications |
ISBN: | 9783319224077 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Operator Theory: Advances and Applications: 251 |
Keywords: | Mathematics , Global analysis (Mathematics) , Manifolds (Mathematics) , Partial differential equations , Differential geometry , Mathematical physics , Mathematics , Partial Differential Equations , Differential Geometry , Global Analysis and Analysis on Manifolds , Mathematical Physics |
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Call number: | SPRINGER-2014-9783319063737:ONLINE Show nearby items on shelf |
Title: | Geometry of Manifolds with Non-negative Sectional Curvature [electronic resource] : Editors: Rafael Herrera, Luis Hernndez-Lamoneda |
Author(s): |
Owen Dearricott Fernando Galaz-Garca Lee Kennard Catherine Searle Gregor Weingart Wolfgang Ziller |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Providing an up-to-date overview of the geometry of manifolds with non-negative sectional curvature, this volume gives a detailed account of the most recent research in the area. The lectures cover a wide range of topics such asgeneral isometric grou p actions, circle actions on positively curved four manifolds, cohomogeneity one actions on Alexandrov spaces, isometric torus actions on Riemannian manifolds of maximal symmetry rank, n-Sasakian manifolds,isoparametric hypersurfaces in spheres, contact C R and CR submanifolds, Riemannian submersions and the Hopf conjecture with symmetry. Also included is an introduction to the theory of exterior differential systems |
Contents: | Riemannian manifolds with positive sectional curvature |
An introduction to isometric group actions | |
A note on maximal symmetry rank, quasipositive curvature and low dimensional manifolds | |
Lectures on n | |
Sasakian manifolds | |
On the Hopf conjecture with symmetry | |
An Introduction to Exterior Differential Systems | |
ISBN: | 9783319063737 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2110 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis , Global differential geometry , Cell aggregation Mathematics |
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Call number: | SPRINGER-2014-9783319052540:ONLINE Show nearby items on shelf |
Title: | Trends in Contemporary Mathematics [electronic resource] |
Author(s): |
Vincenzo Ancona Elisabetta Strickland |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | This book covers a wide spectrum of hot topics and current trends in mathematics, including noncommutative algebra via deformation theory, optimal transportation, nonlinear potential theory,kinetic theory and gas dynamics,geometric numerical integrat ion, finite simple groups of small essential dimension, optimal control problems, extended Dynkin diagrams, spin glasses, aspherical closed manifolds, Boltzmann systems, birational geometry of projectivevarieties and directed graphs, nonlinear diffusion, geometric constructions of extremal metrics on complex manifolds, and Pells equation in polynomials. The book comprises a selection of contributions by leading internationalmathematicians who were speakers at the INdAM Day, an initiative dating back to 20 04 at which the most recent developments in contemporary mathematics are presented |
Contents: | 1 F. Guerra: Interpolation and comparison methods in the mean field spin glass model |
2 A. De Sole, V.G. Kac, D. Valeri: Integrability of dirac reduced Bi | |
Hamiltonian equations | |
3 W. Luck: Some open problems about aspherical closed manifolds abstract | |
4 P. Etingof: Exploring noncommutative algebras via deformation theory | |
5 G. Lancia: Mathematical models and solutions for the analysis of human genotypes | |
6 M. Manetti: Kodaira | |
Spencer formality of products of complex manifolds | |
7 O. Debarre, B. Lass: Monomial transformations of the projective space | |
8 J.L. Vazquez: Progress in the | |
ISBN: | 9783319052540 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer INdAM Series, 2281-518X : v8 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Global analysis (Mathematics) , Differential equations, partial , Computer science Mathematics |
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Call number: | SPRINGER-2014-9783319048079:ONLINE Show nearby items on shelf |
Title: | Analytic and Probabilistic Approaches to Dynamics in Negative Curvature [electronic resource] |
Author(s): |
Franoise Dal'Bo Marc Peign Andrea Sambusetti |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | The work of E. Hopf and G.A. Hedlund, in the 1930s, on transitivity and ergodicity of the geodesic flow for hyperbolic surfaces, marked the beginning of the investigation of the statistical properties and stochastic behavior ofthe flow. The first cen tral limit theorem for the geodesic flow was proved in the 1960s by Y. Sinai for compact hyperbolic manifolds. Since then, strong relationships have been found between the fields of ergodic theory, analysis, andgeometry. Different approaches and new tools have been developed to study the geodesic flow, including measure theory, thermodynamic formalism, transfer operators, Laplace operators, and Brownian motion. All these different points ofview have led to a deep understanding of more general dynamical sy stems, in particular the so-called Anosov systems, with applications to geometric problems such as counting, equirepartition, mixing, and recurrence properties of theorbits. This book comprises two independent texts that provide a self-contained introduct ion to two different approaches to the investigation of hyperbolic dynamics. The first text, by S. Le Borgne, explains the method of martingalesfor the central limit theorem. This approach can be used in several situations, even for weakly hyperbolic flow s, and the author presents a good number of examples and applications to equirepartition and mixing. The second text, by F.Faure and M. Tsujii, concerns the semiclassical approach, by operator theory: chaotic dynamics is described through the spectrum of the associated transfer operator, with applications to the asymptotic counting of periodic orbits. Thebook will be of interest for a broad audience, from PhD and Post-Doc students to experts working on geometry and dynamics |
ISBN: | 9783319048079 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer INdAM Series, 2281-518X : v9 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Operator theory , Global differential geometry , Distribution (Probability theory) |
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Call number: | SPRINGER-2014-9783319021324:ONLINE Show nearby items on shelf |
Title: | Geometric Control Theory and Sub-Riemannian Geometry [electronic resource] |
Author(s): |
Gianna Stefani Ugo Boscain Jean-Paul Gauthier Andrey Sarychev Mario Sigalotti |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | This volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry.On the one hand, Geometric Control Theory used the differential geometric and Lie algebraic language forstudying controllability, mot ion planning,stabilizability and optimality for control systems. The geometric approach turned out to be fruitful in applications to robotics, vision modeling, mathematical physics etc. On the other hand,Riemannian geometry and its generalizations, such a s sub-Riemannian, Finslerian geometry etc., have been actively adopting methods developed in the scope of geometric control. Application of these methods has led to importantresults regarding geometry of sub-Riemannian spaces, regularity of sub-Riemannian distances, properties of the group of diffeomorphisms of sub-Riemannian manifolds, local geometry and equivalence of distributions and sub-Riemannianstructures, regularity of the Hausdorff volume |
Contents: | 1 A. A. Agrachev |
Some open problems | |
2 D. Barilari, A. Lerario | |
Geometry of Maslov cycles | |
3 Y. Baryshnikov, B. Shapiro | |
How to Run a Centipede: a Topological Perspective | |
4 B. Bonnard, O. Cots, L. Jassionnesse | |
Geometric and numerical techniques to compute conjugate and cut loci on Riemannian surfaces | |
5 J | |
B. Caillau, C. Royer | |
On the injectivity and nonfocal domains of the ellipsoid of revolution | |
6 P. Cannarsa, R. Guglielmi | |
Null controllability in large time for the parabolic Grushin operator with singular potential | |
7 Y. Chitour, M. Godoy Molina, P. Kokkonen | |
The rolli | |
ISBN: | 9783319021324 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer INdAM Series, 2281-518X : v5 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis , Global differential geometry , Mathematical optimization |
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Call number: | SPRINGER-2013-9789400753457:ONLINE Show nearby items on shelf |
Title: | Differential Geometry and Mathematical Physics [electronic resource] : Part I. Manifolds, Lie Groups and Hamiltonian Systems |
Author(s): |
Gerd Rudolph Matthias Schmidt |
Date: | 2013 |
Publisher: | Dordrecht : Springer Netherlands : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Starting from an undergraduate level, this book systematically develops the basics of Calculus on manifolds, vector bundles, vector fields and differential forms, Lie groups and Lie group actions, Linear symplecticalgebra and symplectic geometry, Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. Thesecond and third items constitute the link between abstr act calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class andcaustics. The book guides the reader from elementary differential geometry to advan ced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematicaltextbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact |
Note: | Springer eBooks |
Contents: | 1 Differentiable manifolds |
2 Vector bundles | |
3 Vector fields | |
4 Differential forms | |
5 Lie groups | |
6 Lie group actions | |
7 Linear symplectic algebra | |
8 Symplectic geometry | |
9 Hamiltonian systems | |
10 Symmetries | |
11 Integrability | |
12 Hamilton | |
Jacobi theory | |
References | |
ISBN: | 9789400753457 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Theoretical and Mathematical Physics, 1864-5879 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Topological Groups , Global analysis , Global differential geometry , Mathematical physics , Mechanics |
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Call number: | SPRINGER-2013-9783319001289:ONLINE Show nearby items on shelf |
Title: | Hypoelliptic Laplacian and BottChern Cohomology [electronic resource] : A Theorem of RiemannRochGrothendieck in Complex Geometry |
Author(s): |
Jean-Michel Bismut |
Date: | 2013 |
Publisher: | Heidelberg : Springer International Publishing : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The book provides the proof of a complex geometric version of a well-known result in algebraic geometry: the theorem of RiemannRochGrothendieck for proper submersions. It gives an equality of cohomology classes inBottChern cohomology, which is a refi nement for complex manifolds of de Rham cohomology. When the manifolds are Khler, our main result is known. A proof can be given using the elliptic Hodge theory of the fibres, its deformationvia Quillen's superconnections, and a version in families of the 'fantastic cancellations' of McKeanSinger in local index theory. In the general case, this approach breaks down because the cancellations do not occur any more.Onetool used in the book is a deformation of the Hodge theory of the fibres to a hypoelliptic Hodge theory, in such a way that the relevant cohomological information is preserved, and 'fantastic cancellations' do occur for thedeformation. The deformed hypoelliptic Laplacian acts on the total space of the relative tangent bundle of the fibres. Whil e the original hypoelliptic Laplacian discovered by the author can be described in terms of the harmonicoscillator along the tangent bundle and of the geodesic flow, here, the harmonic oscillator has to be replaced by a quartic oscillator.Another idea dev eloped in the book is that while classical elliptic Hodge theory is based on theHermitian product on forms, the hypoelliptic theory involves a Hermitian pairing which is a mild modification of intersection pairing. Probabilistic considerations play an imp ortant role, either as a motivation of some constructions,or in the proofs themselves |
Note: | Springer eBooks |
Contents: | Introduction |
1 The Riemannian adiabatic limit | |
2 The holomorphic adiabatic limit | |
3 The elliptic superconnections | |
4 The elliptic superconnection forms | |
5 The elliptic superconnections forms | |
6 The hypoelliptic superconnections | |
7 The hypoelliptic superconnection forms | |
8 The hypoelliptic superconnection forms of vector bundles | |
9 The hypoelliptic superconnection forms | |
10 The exotic superconnection forms of a vector bundle | |
11 Exotic superconnections and RiemannRochGrothendieck | |
Bibliography | |
Subject Index | |
Index of Notation. | |
ISBN: | 9783319001289 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v305 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , K-theory , Global analysis , Differential equations, partial |
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Call number: | SPRINGER-2013-9783034805858:ONLINE Show nearby items on shelf |
Title: | Pseudo-Differential Operators, Generalized Functions and Asymptotics [electronic resource] |
Author(s): |
Shahla Molahajloo Stevan Pilipovi Joachim Toft M. W Wong |
Date: | 2013 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This volume consists of twenty peer-reviewed papers from the special sessions on pseudodifferential operators and on generalized functions and asymptotics at the Eighth Congress of ISAAC held at the Peoples FriendshipUniversity of Russia in Moscow on August 2227, 2011. The category of papers on pseudo-differential operators contains such topics as elliptic operators assigned to diffeomorphisms of smooth manifolds, analysis on singular manifoldswith edges, heat kernels and Green functions of sub-Lapla cians on the Heisenberg group and Lie groups with more complexities than but closely related to the Heisenberg group, L^p-boundedness of pseudo-differential operators on thetorus, and pseudo-differential operators related to time-frequency analysis. The s econd group of papers contains various classes of distributions and algebras of generalized functions with applications in linear and nonlineardifferential equations, initial value problems and boundary value problems, stochastic and Malliavin-type differ ential equations. This second group of papers is related to the third collection of papers via the setting ofColombeau-type spaces and algebras in which microlocal analysis is developed by means of techniques in asymptotics. The volumecontains the synergi es of the three areas treatedand is a useful complement toitspredecessorspublished in the same series |
Note: | Springer eBooks |
Contents: | Preface |
Elliptic Theory for Operators Associated with Diffeomorphisms of Smooth Manifolds | |
The Singular Functions of Branching Edge Asymptotics | |
The Heat Kernel and Green Function of the Sub | |
Laplacian on the Heisenberg Group | |
Metaplectic Equivalence of the Hierarchical Twisted Laplacian | |
The Heat Kernel and Green Function of a Sub | |
Laplacian on the Hierarchical Heisenberg Group | |
Lp | |
Bounds for Pseudo | |
Differential Operators on the Torus | |
Multiplication Properties in Gelfand | |
Shilov Pseudo | |
Differential Calculus | |
Operator Invariance | |
Initial Value Problems in the Time | |
Frequency Do | |
ISBN: | 9783034805858 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Operator Theory: Advances and Applications : v231 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups , Global analysis , Operator theory , Differential equations, partial |
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Call number: | SPRINGER-2013-9783034805346:ONLINE Show nearby items on shelf |
Title: | Developments of Harmonic Maps, Wave Maps and Yang-Mills Fields into Biharmonic Maps, Biwave Maps and Bi-Yang-Mills Fields [electronic resource] |
Author(s): |
Yuan-Jen Chiang |
Date: | 2013 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Harmonic maps between Riemannian manifolds were first established in 1964. Wave maps are harmonic maps on Minkowski spaces and have been studied since the 1990s. Yang-Mills fields, the critical points of Yang-Mills functionals ofconnections whose cur vature tensors are harmonic, were explored by a few physicists in the 1950s, and biharmonic maps (generalizing harmonic maps) were introducedin 1986. The book presents an overview of the important developmentsmadein these fields since they first came up. Furthermore,it introduces biwave maps (generalizing wave maps) which were first studiedin 2009, and bi-Yang-Mills fields (generalizing Yang-Mills fields) first investigated in 2008.Other topicsdiscussed are exponential harmonic maps, exponential wave maps and exponential Yang-Mills fields |
Note: | Springer eBooks |
Contents: | Preface. 1 Harmonic Maps |
2 Wave Maps | |
3 Yang | |
Mills Fields | |
4 Biharmonic Maps | |
5 Biwave Maps | |
6 Bi | |
Yang | |
Mills Fields | |
7 Exponential Harmonic Maps | |
8 Exponential Wave Maps | |
9.Exponential Yang | |
Mills Connections | |
Index. | |
ISBN: | 9783034805346 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Frontiers in Mathematics, 1660-8046 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis , Differential equations, partial , Global differential geometry , Mathematical optimization |
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Call number: | SPRINGER-2013-9783034803878:ONLINE Show nearby items on shelf |
Title: | Methods of Nonlinear Analysis [electronic resource] : Applications to Differential Equations |
Author(s): |
Pavel Drbek Jaroslav Milota |
Date: | 2013 |
Edition: | 2nd ed. 2013 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | In this book, fundamental methods of nonlinear analysis are introduced, discussed and illustrated in straightforward examples. Each method considered is motivated and explained in its general form, but presented in an abstractframework as comprehensi vely as possible. A large number of methods are applied to boundary value problems for both ordinary and partial differential equations. In this edition we have made minor revisions, added new material andorganized the content slightly differently. In par ticular, we included evolutionary equations and differential equations on manifolds. The applications to partial differential equations follow every abstract framework of the method inquestion. The text is structured in two levels: a self-contained basic level and an advanced level - organized in appendices - for the more experienced reader. The last chapter contains more involved material and can be skipped bythose new to the field. This book serves as both a textbook for graduate-level courses and a ref erence book for mathematicians, engineers and applied scientists. |
Note: | Springer eBooks |
Contents: | Preface |
1 Preliminaries | |
2 Properties of Linear and Nonlinear Operators | |
3 Abstract Integral and Differential Calculus | |
4 Local Properties of Differentiable Mappings | |
5 Topological and Monotonicity Methods | |
6 Variational Methods | |
7 Boundary Value Problems for Partial Differential Equations | |
Summary of Methods | |
Typical Applications | |
Comparison of Bifurcation Results | |
List of Symbols | |
Index | |
Bibliography | |
ISBN: | 9783034803878 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Birkhuser Advanced Texts Basler Lehrbcher |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Functional analysis , Differential equations, partial , Mathematical optimization |
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Call number: | SPRINGER-2013-9781461478676:ONLINE Show nearby items on shelf |
Title: | Introduction to Tensor Analysis and the Calculus of Moving Surfaces [electronic resource] |
Author(s): |
Pavel Grinfeld |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This text is meant to deepen its readers understanding of vector calculus, differential geometry and related subjects in applied mathematics. Designed for advanced undergraduate and graduate students, this text invites itsaudience to take a fresh loo k at previously learned material through the prism of tensor calculus. Once the framework is mastered, the student is introduced to new material which includes differential geometry on manifolds, shapeoptimization, boundary perturbation, and dynamic fluid film equations. Tensor calculus is a powerful tool that combines the geometric and analytical perspectives and enables us to take full advantage of the computational utility ofcoordinate systems. The tensor approach can be of benefit to members of all te chnical sciences including mathematics and all engineering disciplines. If calculus and linear algebra are central to the readers scientific endeavors,tensor calculus is indispensable. The language of tensors, originally championed by Einstein, is as fund amental as the languages of calculus and linear algebra and is one that every technical scientist ought to speak. The tensortechnique, invented at the turn of the 20th century, is now considered classical. Yet, as the author shows, it remains remarkably v ital and relevant. The authors skilled lecturing capabilities are evident by the inclusion ofinsightful examples and a plethora of exercises. A great deal of material is devoted to the geometric fundamentals, the mechanics of change of variables, the prop er use of the tensor notation, and the discussion of the interplaybetween algebra and geometry. The early chapters have many words and few equations. The definition of a tensor comes only in Chapter 6 when the reader is ready for it. While this text main tains a reasonable level of rigor, it takesgreat care to avoid formalizing the subject. The last part of the textbook is devoted to the calculus of moving surfaces. It is the first textboo |
Note: | Springer eBooks |
Contents: | Preface |
Why Tensor Calculus? | |
1. Rules of the Game | |
2. Coordinate Systems and the Role of Tensor Calculus | |
3. Change of Coordinates | |
4. Tensor Description of Euclidean Spaces | |
5. The Tensor Property | |
6. Covariant Differentiation | |
7. Determinants and the Levi | |
Civita Symbol | |
8. Tensor Description of Surfaces | |
9. Covariant Derivative of Tensors with Surface Indices | |
10. The Curvature Tensor | |
11. Covariant Derivative of Tensors with Spatial Indices | |
12. Integration and Gauss's Theorem | |
13. Intrinsic Features of Embedded Surfaces | |
14. Further Topics in Differential Ge | |
ISBN: | 9781461478676 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Matrix theory , Global differential geometry , Mathematical optimization |
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Call number: | SPRINGER-2012-9783642238406:ONLINE Show nearby items on shelf |
Title: | Spectral Analysis on Graph-like Spaces [electronic resource] |
Author(s): |
Olaf Post |
Date: | 2012 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Small-radius tubular structures have attracted considerable attention in the last few years, and are frequently used in different areas such as Mathematical Physics, Spectral Geometry and Global Analysis. In this monograph, weanalyse Laplace-like op erators on thin tubular structures (graph-like spaces''), and their natural limits on metric graphs. In particular, we explore norm resolvent convergence, convergence of the spectra and resonances. Since theunderlying spaces in the thin radius limit chan ge, and become singular in the limit, we develop new tools such as -norm convergence of operators acting in different Hilbert spaces, - an extension of the concept of boundarytriples to partial differential operators, and -an abstract definition of res onances via boundary triples. These tools are formulated in an abstract framework, independent of the original problem of graph-like spaces, so thatthey can be applied in many other situations where the spaces are perturbed |
Note: | Springer eBooks |
Contents: | 1 Introduction |
2 Graphs and associated Laplacians | |
3 Scales of Hilbert space and boundary triples | |
4 Two operators in different Hilbert spaces | |
5 Manifolds, tubular neighbourhoods and their perturbations | |
6 Plumbers shop: Estimates for star graphs and related spaces | |
7 Global convergence results | |
ISBN: | 9783642238406 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2039 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Functional analysis , Operator theory , Differential equations, partial |
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Call number: | SPRINGER-2012-9783642236693:ONLINE Show nearby items on shelf |
Title: | Complex MongeAmpre Equations and Geodesics in the Space of Khler Metrics [electronic resource] |
Author(s): |
Vincent Guedj |
Date: | 2012 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The purpose of these lecture notes is to provide an introduction to the theory of complex MongeAmpre operators (definition, regularity issues, geometric properties of solutions, approximation) on compact Khler manifolds(with or without boundary). The se operators are of central use in several fundamental problems of complex differential geometry (KhlerEinstein equation, uniqueness of constant scalar curvature metrics), complex analysis anddynamics. The topics covered include, the Dirichlet problem (af ter BedfordTaylor), MongeAmpre foliations and laminated currents, polynomial hulls and Perron envelopes with no analytic structure, a self-contained presentation ofKrylov regularity results, a modernized proof of the CalabiYau theorem (after Yau and Kolod ziej), an introduction to infinite dimensional riemannian geometry, geometric structures on spaces of Khler metrics (after Mabuchi, Semmesand Donaldson), generalizations of the regularity theory of CaffarelliKohnNirenbergSpruck (after Guan, Chen and Block i) and Bergman approximation of geodesics (after PhongSturm and Berndtsson). Each chapter can be readindependently and is based on a series of lectures byR. Berman, Z. Blocki, S. Boucksom, F. Delarue, R. Dujardin, B. Kolev and A. Zeriahi, delivered to non -experts. The book is thus addressed to any mathematician with some interest inone of the following fields, complex differential geometry, complex analysis, complex dynamics, fully non-linear PDE's and stochastic analysis |
Note: | Springer eBooks |
Contents: | 1.Introduction |
I. The Local Homogenious Dirichlet Problem | |
2. Dirichlet Problem in Domains of Cn | |
3. Geometric Maximality | |
II. Stochastic Analysis for the Monge | |
Ampre Equation | |
4. Probabilistic Approach to Regularity | |
III. Monge | |
Ampre Equations on Compact Manifolds | |
5.The Calabi | |
Yau Theorem | |
IV Geodesics in the Space of Khler Metrics | |
6. The Riemannian Space of Khler Metrics | |
7. MA Equations on Manifolds with Boundary | |
8. Bergman Geodesics | |
ISBN: | 9783642236693 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2038 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Differential equations, partial , Global differential geometry |
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Call number: | SPRINGER-2012-9783034803762:ONLINE Show nearby items on shelf |
Title: | Yamabe-type Equations on Complete, Noncompact Manifolds [electronic resource] |
Author(s): |
Paolo Mastrolia Marco Rigoli Alberto G Setti |
Date: | 2012 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The aim of this monograph is to present a self-contained introduction to some geometric and analytic aspects of the Yamabe problem. The book also describes a wide range of methods and techniques that can be successfully applied tononlinear differenti al equations in particularly challenging situations. Such situations occur where the lack of compactness, symmetry and homogeneity prevents the use of more standard tools typically used in compact situations or forthe Euclidean setting. The work is writte n in an easy style that makes it accessible even to non-specialists. After a self-contained treatment of the geometric tools used in the book, readers are introduced to the main subject by meansof a concise but clear study of some aspects of the Yamabe pr oblem on compact manifolds. This study provides the motivation and geometrical feeling for the subsequent part of the work. In the main body of the book, it is shown how thegeometry and the analysis of nonlinear partial differential equations blend togeth er to give up-to-date results on existence, nonexistence, uniqueness and a priori estimates for solutions of general Yamabe-type equations andinequalities on complete, non-compact Riemannian manifolds |
Note: | Springer eBooks |
Contents: | Introduction |
1 Some Riemannian Geometry | |
2 Pointwise conformal metrics | |
3 General nonexistence results | |
4 A priori estimates | |
5 Uniqueness | |
6 Existence | |
7 Some special cases | |
References | |
Index | |
ISBN: | 9783034803762 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v302 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis , Global differential geometry |
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Call number: | SPRINGER-2012-9783034802574:ONLINE Show nearby items on shelf |
Title: | Metric and Differential Geometry [electronic resource] : The Jeff Cheeger Anniversary Volume |
Author(s): |
Xianzhe Dai Xiaochun Rong |
Date: | 2012 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Metric and Differential Geometry grew out ofa similarly named conference held at Chern Institute of Mathematics, Tianjin and Capital Normal University, Beijing. The various contributions in this volume cover a broad range oftopics in metric and diffe rential geometry, including metric spaces, Ricci flow, Einstein manifolds, Khler geometry, index theory, and hypoelliptic Laplacian and analytic torsion. The book includes papers on the most recent advancesas well as survey articles on new developments. C ontributors: M.T. Anderson J.-M. Bismut X. Chen X. Dai R. Harvey P. Koskela B. Lawson X. Ma R. Melrose W. Mller A. Naor J. Simons C. Sormani D. Sullivan S. Sun G. Tian K. Wildrick W.Zhang |
Note: | Springer eBooks |
Contents: | Preface |
Blaine Lawson, Early Work of Jeff Cheeger | |
Mike Anderson, Boundary value problems for metrics on 3 | |
manifolds | |
Xiuxiong Chen and Song Sun, Space of Kaehler metrics (V) Kaehler quantization | |
Reese Harvey and Blaine Lawson, Split special Lagrangian geometry | |
Christina Sormani, How Riemannian manifolds converge: a survey | |
Gang Tian, Existence of Einstein metrics on Fano manifolds | |
Pekka Koskela and K. Wildrick, Analytic properties of quasiconformal mappings between metric spaces | |
Assaf Naor, An application of metric cotype to quasisymmetric embeddings | |
Jean | |
Michel Bi | |
ISBN: | 9783034802574 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v297 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , K-theory , Global analysis , Geometry , Global differential geometry |
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Call number: | SPRINGER-2012-9781461436584:ONLINE Show nearby items on shelf |
Title: | The General Theory of Relativity [electronic resource] A Mathematical Exposition |
Author(s): |
Anadijiban Das Andrew DeBenedictis |
Date: | 2012 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
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Note: | The General Theory of Relativity: A Mathematical Exposition will serve readers as a modern mathematical introduction to the general theory of relativity. Throughout the book, examples, worked-out problems, and exercises (withhints and solutions) are furnished. Topics in this book include, but are not limited to: tensor analysis the special theory of relativity the general theory of relativity and Einsteins field equations sphericallysymmetric solutions and experimental confirmations static and s tationary space-time domains black holes cosmological models algebraic classifications and the Newman-Penrose equations the coupledEinstein-Maxwell-Klein-Gordon equations appendices covering mathematical supplements and special topics Mathematical ri gor, yet very clear presentation of the topics make this book a unique text for both university students andresearch scholars. Anadijiban Das has taught courses on Relativity Theory at The University College of Dublin, Ireland Jadavpur University, India C arnegie-Mellon University, USA and Simon Fraser University, Canada. His major areasof research include, among diverse topics, the mathematical aspects of general relativity theory. Andrew DeBenedictis has taught courses in Theoretical Physics at Simon Fra ser University, Canada, and is also a member of The PacificInstitute for the Mathematical Sciences. His research interests include quantum gravity, classical gravity, and semi-classical gravity |
Note: | Springer eBooks |
Contents: | Tensor Analysis on Differentiable Manifolds |
The Pseudo | |
Riemannian Space | |
Time Manifold M4 | |
Spherically Symmetric Space | |
Time Domains | |
Static and Stationary Space | |
Time Domains | |
Black Holes | |
Cosmology | |
Algebraic Classification of Field Equations | |
The Coupled Einstein | |
Maxwell | |
Klein | |
Gordon Equations | |
Appendix 1: Variational Derivation of Differential Equations | |
Appendix 2: Partial Differential Equations | |
Appendix 3: Canonical Forms of Matrices | |
Appendix 4: Conformally Flat Space | |
Times and the Fifth Force | |
Appendix 5: Linearized Theory and Gravitational Waves | |
Appendix 6: | |
ISBN: | 9781461436584 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Global analysis |
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Call number: | SPRINGER-2012-9781461436577:ONLINE Show nearby items on shelf |
Title: | The General Theory of Relativity [electronic resource] |
Author(s): |
Anadijiban Das Andrew DeBenedictis |
Date: | 2012 |
Publisher: | Springer New York |
Size: | 1 online resource |
Note: | Monograph |
Note: | Springer 2012 Physics and Astronomy eBook collection |
Note: | Springer e-book platform |
ISBN: | 9781461436577 |
Series: | e-books |
Keywords: | Classical and Quantum Gravitation, Relativity Theory , Mathematical Physics , Cosmology , Mathematical Applications in the Physical Sciences , Global Analysis and Analysis on Manifolds |
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Call number: | SPRINGER-2012-9781441999825:ONLINE Show nearby items on shelf |
Title: | Introduction to Smooth Manifolds [electronic resource] |
Author(s): |
John M Lee |
Date: | 2012 |
Edition: | 2nd ed. 2012 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book is an introductory graduate-level textbook on the theory of smooth manifolds. Its goal is to familiarize students with the tools they will need in order to use manifolds in mathematical or scientific researchsmoothstructures, tangent vector s and covectors, vector bundles, immersed and embedded submanifolds, tensors, differential forms, de Rham cohomology, vector fields, flows, foliations, Lie derivatives, Lie groups, Lie algebras, and more. Theapproach is as concrete as possible, with pictu res and intuitive discussions of how one should think geometrically about the abstract concepts, while making full use of the powerful tools that modern mathematics has to offer. Thissecond edition has been extensively revised and clarified, and the topic s have been substantially rearranged. The book now introduces the two most important analytic tools, the rank theorem and the fundamental theorem on flows, muchearlier so that they can be used throughout the book. A few new topics have been added, notably Sards theorem and transversality, a proof that infinitesimal Lie group actions generate global group actions, a more thorough study offirst-order partial differential equations, a brief treatment of degree theory for smooth maps between compact manifolds , and an introduction to contact structures. Prerequisites include a solid acquaintance with general topology, thefundamental group, and covering spaces, as well as basic undergraduate linear algebra and real analysis |
Note: | Springer eBooks |
Contents: | Preface |
1 Smooth Manifolds | |
2 Smooth Maps | |
3 Tangent Vectors | |
4 Submersions, Immersions, and Embeddings | |
5 Submanifolds | |
6 Sard's Theorem | |
7 Lie Groups | |
8 Vector Fields | |
9 Integral Curves and Flows | |
10 Vector Bundles | |
11 The Cotangent Bundle | |
12 Tensors | |
13 Riemannian Metrics | |
14 Differential Forms | |
15 Orientations | |
16 Integration on Manifolds | |
17 De Rham Cohomology | |
18 The de Rham Theorem | |
19Distributions and Foliations | |
20 The Exponential Map | |
21 Quotient Manifolds | |
22 Symplectic Manifolds | |
Appendix A: Review of Topology | |
Appendix B: Review | |
ISBN: | 9781441999825 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Graduate Texts in Mathematics, 0072-5285 : v218 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global differential geometry |
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Call number: | SPRINGER-2012-9780817683436:ONLINE Show nearby items on shelf |
Title: | Singularities of Differentiable Maps, Volume 2 [electronic resource] : Monodromy and Asymptotics of Integrals |
Author(s): |
V.I Arnold S.M Gusein-Zade A.N Varchenko |
Date: | 2012 |
Publisher: | Boston : Birkhuser Boston : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Originally published inthe 1980s, Singularities of DifferentiableMaps: Monodromy and Asymptotics of Integrals was thesecond oftwovolumes that togetherformed a translation of the authors'influential Russian monographon singularity theory.This uncorrec ted softcover reprint of the work brings its still-relevant content back into the literature, making it availableand affordableto a global audience of researchers and practitioners. Whilethe first volume of this title, subtitled Classification of Critical Points, Caustics and Wave Fronts, contained the zoology of differentiable mapsthat is, was devoted to a description of what, where, and how singularities could beencounteredthis second volume concentrates on elements of theanatomy and physiology of singu larities of differentiable functions. The questions considered here are about the structure of singularities and how they function. Inthe first part the authors consider the topological structure of isolated critical points of holomorphic functions: vanis hing cycles distinguished bases intersection matricesmonodromy groupsthe variation operatorand theirinterconnections and method of calculation. The second part is devoted to the study of the asymptotic behavior of integrals of the method of stationary pha se, which is widely met within applications. The third and last part dealswith integrals evaluated over level manifolds in a neighborhood of the critical point of a holomorphic function. Thismonograph is suitablefor mathematicians, researchers, postgradua tes, and specialists in the areas ofmechanics, physics, technology, and other sciences dealing with the theory of singularities of differentiable maps |
Note: | Springer eBooks |
Contents: | Part I. The topological structure of isolated critical points of functions |
Introduction | |
Elements of the theory of Picard | |
Lefschetz | |
The topology of the non | |
singular level set and the variation operator of a singularity | |
The bifurcation sets and the monodromy group of a singularity | |
The intersection matrices of singularities of functions of two variables | |
The intersection forms of boundary singularities and the topology of complete intersections | |
Part II. Oscillatory integrals | |
Discussion of results | |
Elementary integrals and the resolution of singularities of the phase | |
As | |
ISBN: | 9780817683436 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Modern Birkhuser Classics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Topological Groups , Global analysis (Mathematics) , Global differential geometry , Cell aggregation Mathematics |
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Call number: | SPRINGER-2012-9780817682774:ONLINE Show nearby items on shelf |
Title: | Perspectives in Analysis, Geometry, and Topology [electronic resource] : On the Occasion of the 60th Birthday of Oleg Viro |
Author(s): |
Ilia Itenberg Burglind Jricke Mikael Passare |
Date: | 2012 |
Edition: | 1 |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | A Marcus Wallenberg Symposium on Perspectives in Analysis, Geometry, and Topology was held at Stockholm University in May 2008. The choice of subjects of the Symposium and present volume was motivated by the work and mathematicalinterests of Oleg Vir o to whom the Symposium and this volume are dedicated. As a professor of Uppsala University, Viro has made invaluable contributions to Swedish research by complementing the country's longstanding tradition inanalysis with his own renowned expertise in geo metry and topology. Consolidating in a single volume a major portion of the recent, impressive encounters among the fields of analysis, geometry, and topology would be too ambitious. Thecollection of papers in this work still should give some sense of the development of the fields and their interactions. The topics presented by leading experts in their respective fields include: algebraic geometry, in particular, realalgebraic geometry, differential geometry, symplectic and contact geometry, complex analy sis, three- and four-dimensional manifolds, and invariants of links. Also included in the book is the opening speech of the Symposium by LennartCarleson on the Unity of Mathematics. Contributors: S. Akbulut K. Baker R. Berman A. Degtyarev J.-P. Demailly T . Ekholm Y. Eliashberg M. Entov J. Etnyre D. Gay G. Henkin I. Itenberg L. Kauffman K. Kaveh M. Khanevsky V. Kharlamov A.Khovanskii C. Manolescu N. Mishachev N. Mok S. Orevkov L. Polterovich P. Py N. Reshetikhin A. Shumakovitch E. Shustin A. Stipsicz C. St roppel B. Webster C. Woodward |
Note: | Springer eBooks |
Contents: | Preface |
1 Selman Akbulut, Exotic structures on smooth 4 | |
manifolds | |
2 Kenneth Baker, John Etnyre, Rational linking and contact geometry | |
3 Robert Berman, Jean | |
Pierre Demailly, Regularity of plurisubharmonic upper envelopes in big cohomology classes | |
4 Alex Degtarev, Towards the generalized Shapiro and Shapiro conjecture | |
5 Alex Degtarev, Ilia Itenberg, Viatcheslav Kharlamov, On the number of components of a complete intersection of real quadrics | |
6 Tobias Ekholm, Rational Symplectic Field Theory and linearized Legendrian contact homology | |
7 Yakov Eliashberg, N. Mishachev, Wrinkling | |
ISBN: | 9780817682774 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v296 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Global analysis , Geometry , Topology |
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Call number: | SPRINGER-2012-9780817646936:ONLINE Show nearby items on shelf |
Title: | An Introduction to Riemann Surfaces [electronic resource] |
Author(s): |
Terrence Napier Mohan Ramachandran |
Date: | 2012 |
Publisher: | Boston, MA : Birkhuser Boston : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This textbook presents a unified approach to compact and noncompact Riemann surfaces from the point of view of the L -method, a powerful technique used in the theory of several complex variables. The work features a simpleconstruction of a strictly s ubharmonic exhaustion function and a related construction of a positive-curvature Hermitian metric in a holomorphic line bundle, topics which serve as starting points for proofs of standard results such asthe Mittag-Leffler, Weierstrass, and Runge theorem s the RiemannRoch theorem the Serre duality and Hodge decomposition theorems and the uniformization theorem. The book also contains treatments of other facts concerning theholomorphic, smooth, and topological structure of a Riemann surface, such as the bi holomorphic classification of Riemann surfaces, the embedding theorems, the integrability of almost complex structures, the Schnflies theorem (and theJordan curve theorem), and the existence of smooth structures on second countable surfaces. Although some previous experience with complex analysis, Hilbert space theory, and analysis on manifolds would be helpful, the onlyprerequisite for this book is a working knowledge of point-set topology and elementary measure theory. The work includes numerous exercis esmany of which lead to further development of the theoryand presents (with proofs)streamlined treatments of background topics from analysis and topology on manifolds in easily-accessible reference chapters, making it ideal for a one- or two-semester grad uate course |
Note: | Springer eBooks |
Contents: | Preface |
Introduction | |
Complex analysis in C | |
Riemann Surfaces and the L2 \delta | |
Method for Scalar | |
Valued Forms | |
The L2 \delta | |
Method in a Holomorphic Line Bundle | |
Compact Riemann Surfaces | |
Uniformization and Embedding ofRiemann Surfaces | |
Holomorphic Structures on Topological Surfaces | |
Background Material on Analysis in Rnand Hilbert Space Theory | |
Background Material on Linear Algebra | |
Background Material on Manifolds | |
Background Material on Fundamental Groups, Covering Spaces, and (Co)homology | |
Background Material on Sobolev Spaces and Regularity | |
References | |
Not | |
ISBN: | 9780817646936 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Cornerstones |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Global analysis , Differential equations, partial |
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Call number: | SPRINGER-2011-9783642162862:ONLINE Show nearby items on shelf |
Title: | The Ricci Flow in Riemannian Geometry [electronic resource] A Complete Proof of the Differentiable 1/4-Pinching Sphere Theorem |
Author(s): |
Ben Andrews Christopher Hopper |
Date: | 2011 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book focuses on Hamilton's Ricci flow, beginning with a detailed discussion of the required aspects of differential geometry, progressing through existence and regularity theory, compactness theorems for Riemannian manifolds,and Perelman's nonco llapsing results, and culminating in a detailed analysis of the evolution of curvature, where recent breakthroughs of Bhm and Wilking and Brendle and Schoen have led to a proof of the differentiable 1/4-pinchingsphere theorem |
Note: | Springer eBooks |
Contents: | 1 Introduction |
2 Background Material | |
3 Harmonic Mappings | |
4 Evolution of the Curvature | |
5 Short | |
Time Existence | |
6 Uhlenbecks Trick | |
7 The Weak Maximum Principle | |
8 Regularity and Long | |
Time Existence | |
9 The Compactness Theorem for Riemannian Manifolds | |
10 The F | |
Functional and Gradient Flows | |
11 The W | |
Functional and Local Noncollapsing | |
12 An Algebraic Identity for Curvature Operators | |
13 The Cone Construction of Bhm and Wilking | |
14 Preserving Positive Isotropic Curvature | |
15 The Final Argument | |
ISBN: | 9783642162862 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2011 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis , Differential equations, partial , Global differential geometry |
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Call number: | SPRINGER-2011-9783642155642:ONLINE Show nearby items on shelf |
Title: | Sobolev Spaces [electronic resource] : with Applications to Elliptic Partial Differential Equations |
Author(s): |
Vladimir Maz'ya |
Date: | 2011 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Sobolev spaces play an outstanding role in modern analysis, in particular, in the theory of partial differential equations and its applications in mathematical physics. They form an indispensable tool in approximation theory,spectral theory, differen tial geometry etc. The theory of these spaces is of interest in itself being a beautiful domain of mathematics. The present volume includes basics on Sobolev spaces, approximation and extension theorems,embedding and compactness theorems, their relations with isoperimetric and isocapacitary inequalities, capacities with applications to spectral theory of elliptic differential operators as well as pointwise inequalities forderivatives. The selection of topics is mainly influenced by the authors involvement in their study, a considerable part of the text is a report on his work in the field. Part of this volume rst appeared in German as threebooklets of Teubner-Texte zur Mathematik (1979,1980). In the Springer volume Sobolev Spaces, published in English in 1985, the material was expanded and revised. The present 2nd edition is enhanced by many recent results and itincludes new applications to linear and nonlinear partial differential equations. New historical comments, five new chapters and a signicantly au gmented list of references aim to create a broader and modern view of the area |
Note: | Springer eBooks |
Contents: | Introduction |
1 .Basic Properties of Sobolev Spaces | |
2 .Inequalities for Functions Vanishing at the Boundary | |
3.Conductor and Capacitary Inequalities with Applications to Sobolev | |
type Embeddings | |
4.Generalizations for Functions on Manifolds and Topological Spaces | |
5.Integrability of Functions in the Space L 1/1() | |
6.Integrability of Functions in the Space L 1/p () | |
7.Continuity and Boundedness of Functions in Sobolev Spaces | |
8.Localization Moduli of Sobolev Embeddings for General Domains | |
9.Space of Functions of Bounded Variation | |
10.Certain Function Spaces, Capacities | |
ISBN: | 9783642155642 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 0072-7830 : v342 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) |
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Call number: | SPRINGER-2011-9783642110740:ONLINE Show nearby items on shelf |
Title: | Pseudo-differential Operators [electronic resource] |
Author(s): |
Louis Nirenberg |
Date: | 2011 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | S. Agmon: Asymptotic formulas with remainder estimates for eigenvalues of elliptic operators.- J. Bokobza-Haggiag: Une dfinition globale des oprateurs pseudo-diffrentiels sur une varit diffrentiable.- L. Boutet deMonvel: Pseudo-differential operators and analytic function.- A. Calderon: A priori estimates for singular integral operators.- B.F. Jones: Characterization of spaces of Bessel potentials related to the heat equation.- J.J. Kohn:Pseudo-differential operators and non-elliptic problems.- R.T. Seeley: Topics in pseudo-differential operators.- I.M. E. Shamir: Boundary value problems for elliptic convolution systems.- Singer: Elliptic operators on manifolds |
Note: | Springer eBooks |
Contents: | S. Agmon: Asymptotic formulas with remainder estimates for eigenvalues of elliptic operators |
J. Bokobza | |
Haggiag: Une dfinition globale des oprateurs pseudo | |
diffrentiels sur une varit diffrentiable | |
L. Boutet de Monvel: Pseudo | |
differential operators and analytic function | |
A. Calderon: A priori estimates for singular integral operators | |
B.F. Jones: Characterization of spaces of Bessel potentials related to the heat equation | |
J.J. Kohn: Pseudo | |
differential operators and non | |
elliptic problems | |
R.T. Seeley: Topics in pseudo | |
differential operators | |
I.M. E. Shamir: Boundary | |
ISBN: | 9783642110740 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | C.I.M.E. Summer Schools : v47 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis , Operator theory , Differential equations, partial |
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Call number: | SPRINGER-2011-9783642109980:ONLINE Show nearby items on shelf |
Title: | Problems in Non-Linear Analysis [electronic resource] |
Author(s): |
G Prodi |
Date: | 2011 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | H. Brezis: Proprits rgularisantes de certains semigroupes et applications.- F. Browder: Normal solvability and existence theorems for nonlinear mappings in Banach spaces.- F. Browder: Normal solvability for nonlinearmappings and the geometry of Banac h spaces.- J. Eells, K.D. Elworthy: Wiener integration on certain manifolds.- W.H. Fleming: Nonlinear partial differential equations - Probabilistic and game theoretic methods.- C. Foias: Solutionsstatistiques des quations dvolution non linaires.- J.L. Li ons: Quelques problmes de la thorie des quations non linaires dvolution.- A. Pazy: Semi-groups of nonlinear contractions in Hilbert space.- R. Temam:Equations aux drives partielles stochastiques.- M.M. Vainberg: Le problme de la minimisation des fonctionn elles non linaires |
Note: | Springer eBooks |
Contents: | H. Brezis: Proprits rgularisantes de certains semigroupes et applications |
F. Browder: Normal solvability and existence theorems for nonlinear mappings in Banach spaces | |
F. Browder: Normal solvability for nonlinear mappings and the geometry of Banach spaces | |
J. Eells, K.D. Elworthy: Wiener integration on certain manifolds | |
W.H. Fleming: Nonlinear partial differential equations | |
Probabilistic and game theoretic methods | |
C. Foias: Solutions statistiques des quations dvolution non linaires | |
J.L. Lions: Quelques problmes de la thorie des quations non linaires d | |
ISBN: | 9783642109980 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | C.I.M.E. Summer Schools : v55 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis |
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Call number: | SPRINGER-2011-9783642109553:ONLINE Show nearby items on shelf |
Title: | Spectral Analysis [electronic resource] |
Author(s): |
Jaures Cecconi |
Date: | 2011 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | G. Bottaro: Quelques rsultats danalyse spectrale pour des oprateurs diffrentiels coefficients constants sur des domaines non borns.- L. Grding: Eigenfuction expansions.- C. Goulaouic: Valeurs propres de problmesaux limites irrguliers: applications.- G. Grubb: Essential spectra of elliptic systems on compact manifolds.- J.Cl. Guillot: Quelques rsultats rcents en Scattering.- N. Schechter: Theory of perturbations of partial differentialoperators.- C.H. Wilcox: Spectral analysis of the Laplacian with a discontinuous coefficient |
Note: | Springer eBooks |
Contents: | G. Bottaro: Quelques rsultats danalyse spectrale pour des oprateurs diffrentiels coefficients constants sur des domaines non borns |
L. Grding: Eigenfuction expansions | |
C. Goulaouic: Valeurs propres de problmes aux limites irrguliers: applications | |
G. Grubb: Essential spectra of elliptic systems on compact manifolds | |
J.Cl. Guillot: Quelques rsultats rcents en Scattering | |
N. Schechter: Theory of perturbations of partial differential operators | |
C.H. Wilcox: Spectral analysis of the Laplacian with a discontinuous coefficient | |
ISBN: | 9783642109553 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | C.I.M.E. Summer Schools : v64 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) |
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Call number: | SPRINGER-2011-9783034801454:ONLINE Show nearby items on shelf |
Title: | Lecture Notes on Mean Curvature Flow [electronic resource] |
Author(s): |
Carlo Mantegazza |
Date: | 2011 |
Publisher: | Basel : Springer Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book is an introduction to the subject of mean curvature flow of hypersurfaces with special emphasis on the analysis of singularities. This flow occurs in the description of the evolution of numerous physical models where theenergy is given by t he area of the interfaces. These notes provide a detailed discussion of the classical parametric approach (mainly developed by R. Hamilton and G. Huisken). They are well suited for a course at PhD/PostDoc level andcan be useful for any researcher interest ed in a solid introduction to the technical issues of the field. All the proofs are carefully written, often simplified, and contain several comments. Moreover, the author revisited andorganized a large amount of material scattered around in literature in the last 25 years |
Note: | Springer eBooks |
Contents: | Foreword |
Chapter 1. Definition and Short Time Existence | |
Chapter 2. Evolution of Geometric Quantities | |
Chapter 3. Monotonicity Formula and Type I Singularities | |
Chapter 4. Type II Singularities | |
Chapter 5. Conclusions and Research Directions | |
Appendix A. Quasilinear Parabolic Equations on Manifolds | |
Appendix B. Interior Estimates of Ecker and Huisken | |
Appendix C. Hamiltons Maximum Principle for Tensors | |
Appendix D. Hamiltons Matrix LiYauHarnack Inequality in Rn | |
Appendix E. Abresch and Langer Classification of Homothetically Shrinking Closed Curves | |
Appendix | |
ISBN: | 9783034801454 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v290 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) |
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Call number: | SPRINGER-2011-9781461414995:ONLINE Show nearby items on shelf |
Title: | Hamiltonian Structures and Generating Families [electronic resource] |
Author(s): |
Sergio Benenti |
Date: | 2011 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book is an enhanced version of an earlier Russian edition. Besides thorough revisions, more emphasis was put on reordering the topics according to a category-theoretical view. This allows the mathematical results to bestated, proved, and underst ood in a much easier and elegant way. From the reviews of the Russian edition: The main accent is shifted to the application. . .in geometrical optics, thermostatics and control theory, and not to theHamiltonian mechanics only. . . . To make the book fair ly self-contained, full details of basic definitions and all proofs are included. In this way, the majority of the text can be read without the prerequisite of a course ingeometry. The excellent collection of examples illustrates the relatively hard and h ighly abstract mathematical theory and its hidden difficulties.. . .The book can rise real interest for specialists . . . . The . . . book is asignificant input in the modern symplectic geometry and its applications. (Andrey Tsiganov, St. Petersburg State University) Sergio Benenti is a professor of mathematical physics at Universit di Torino, Italy. His current fields ofresearch include symplectic geometry with applications to physical theories, Riemannian geometry with applications to the theory of the separation of variables in the Hamilton-Jacobi equation and in other relevant differentialequations of physics, and mathematical models of the dynamics of non-holonomic systems |
Note: | Springer eBooks |
Contents: | Preface |
Basic Notions of Calculus on Manifolds | |
Relations | |
Symplectic Relations on Symplectic Manifolds | |
Symplectic Relations on Cotangent Bundles | |
Canonical Lift on Cotangent Bundles | |
The Geometry of the Hamilton | |
Jacobi Equation | |
Hamiltonian Optics in Euclidean Spaces | |
Control of Static Systems | |
Supplementary Topics | |
Global Hamilton Principal Functions on S2 and H2 | |
References | |
Index | |
ISBN: | 9781461414995 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext, 0172-5939 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis , Systems theory , Global differential geometry |
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Call number: | SPRINGER-2011-9781461411055:ONLINE Show nearby items on shelf |
Title: | An Invitation to Morse Theory [electronic resource] |
Author(s): |
Liviu Nicolaescu |
Date: | 2011 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
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Note: | This self-contained treatment of Morse theory focuses on applications and is intended for a graduate course on differential or algebraic topology. The book is divided into three conceptually distinct parts. The first part containsthe foundations of M orse theory. The second part consists of applications of Morse theory over the reals, while the last part describes the basics and some applications of complex Morse theory, a.k.a. Picard-Lefschetz theory. Thisis the first textbook to include topics such as Morse-Smale flows, Floer homology, min-max theory, moment maps and equivariant cohomology, and complex Morse theory. The exposition is enhanced with examples, problems, and illustrations,and will be of interest to graduate students as well as research ers. The reader is expected to have some familiarity with cohomology theory and with the differential and integral calculus on smooth manifolds. Some features of thesecond edition include added applications, such as Morse theory and the curvature of knot s, the cohomology of the moduli space of planar polygons, and the Duistermaat-Heckman formula. The second edition also includes a new chapter onMorse-Smale flows and Whitney stratifications, many new exercises, and various corrections from the first editi on |
Note: | Springer eBooks |
Contents: | Preface |
Notations and Conventions | |
1 Morse Functions | |
2 The Topology of Morse Functions | |
3 Applications | |
4 Morse | |
Smale Flows and Whitney Stratifications | |
5 Basics of Complex Morse Theory | |
6 Exercises and Solutions | |
References | |
Index | |
ISBN: | 9781461411055 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext, 0172-5939 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis , Global differential geometry , Cell aggregation Mathematics |
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Call number: | SPRINGER-2011-9781441974006:ONLINE Show nearby items on shelf |
Title: | An Introduction to Manifolds [electronic resource] |
Author(s): |
Loring W Tu |
Date: | 2011 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Manifolds, the higher-dimensional analogues of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classicalmechanics, general relativity , and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By theend of the book the reader should be able to comput e, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way the reader acquires the knowledge and skills necessaryfor further study of geometry and topology. The second edition contains fifty pages of new material. Many passages have been rewritten, proofs simplified, and new examples and exercises added. This work may be used as a textbook for aone-semester graduate or advanced undergraduate course, as well as by students engaged in sel f-study. The requisite point-set topology is included in an appendix of twenty-five pages other appendices review facts from real analysisand linear algebra. Hints and solutions are provided to many of the exercises and problems. Requiring only minimal un dergraduate prerequisites, An Introduction to Manifolds is also an excellent foundation for the author'spublication with Raoul Bott, Differential Forms in Algebraic Topology. |
Note: | Springer eBooks |
Contents: | Preface to the Second Edition |
Preface to the First Edition | |
Chapter 1. Euclidean Spaces | |
Chapter 2. Manifolds | |
Chapter 3. The Tangent Space | |
Chapter 4. Lie Groups and Lie Algebras | |
Chapter 5. Differential Forms | |
Chapter 6. Integration | |
Chapter 7. De Rham Theory | |
Appendices | |
A. Point | |
Set Topology | |
B. The Inverse Function Theorem on R(N) and Related Results | |
C. Existence of a Partition of Unity in General | |
D. Linear Algebra | |
E. Quaternions and the Symplectic Group | |
Solutions to Selected Exercises | |
Hints and Solutions to Selected End | |
of | |
Section Problems | |
List of Sym | |
ISBN: | 9781441974006 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext, 0172-5939 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis , Global differential geometry , Cell aggregation Mathematics |
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Call number: | SPRINGER-2011-9780857291639:ONLINE Show nearby items on shelf |
Title: | Global and Stochastic Analysis with Applications to Mathematical Physics [electronic resource] |
Author(s): |
Yuri E Gliklikh |
Date: | 2011 |
Publisher: | London : Springer London |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Methods of global analysis and stochastic analysis are most often applied in mathematical physics as separate entities, thus forming important directions in the field. However, while combination of the two subject areas is rare,it is fundamental for the consideration of a broader class of problems This book develops methods of Global Analysis and Stochastic Analysis such that their combination allows one to have a more or less common treatment for areas ofmathematical physics that traditionally are c onsidered as divergent and requiring different methods of investigation Global and Stochastic Analysis with Applications to Mathematical Physics covers branches of mathematics that arecurrently absent in monograph form. Through the demonstration of new to pics of investigation and results, both in traditional and more recent problems, this book offers a fresh perspective on ordinary and stochastic differentialequations and inclusions (in particular, given in terms of Nelson's mean derivatives) on linear sp aces and manifolds. Topics covered include classical mechanics on non-linear configuration spaces, problems of statistical and quantumphysics, and hydrodynamics A self-contained book that provides a large amount of preliminary material and recent results which will serve to be a useful introduction to the subject and a valuable resource for further research. It willappeal to researchers, graduate and PhD students working in global analysis, stochastic analysis and mathematical physics |
Note: | Springer eBooks |
Contents: | Part I Global Analysis |
Manifolds and Related Objects | |
Connections | |
Ordinary Differential Equations | |
Elements of the Theory of Set | |
Valued Mappings | |
Analysis on Groups of Diffeomorphisms | |
Part II Stochastic Analysis | |
Essentials from Stochastic Analysis in Linear Spaces | |
Stochastic Analysis on Manifolds | |
Mean Derivatives in Linear Spaces | |
Mean Derivatives on Manifolds | |
Stochastic Analysis on Groups of Diffeomorphism | |
Part III Applications to Mathematical Physics | |
Newtonian Mechanics | |
Accessible Points and Sub | |
Manifolds of Mechanical Systems. Controllability | |
Some Pr | |
ISBN: | 9780857291639 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Theoretical and Mathematical Physics, 1864-5879 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Mathematics , Global analysis , Distribution (Probability theory) , Mathematical physics |
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Call number: | SPRINGER-2011-9780857290304:ONLINE Show nearby items on shelf |
Title: | Holomorphic Function Theory in Several Variables [electronic resource] : An Introduction |
Author(s): |
Christine Laurent-Thibaut |
Date: | 2011 |
Publisher: | London : Springer London |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book provides an introduction to complex analysis in several variables. The viewpoint of integral representation theory together with Grauert's bumping method offers a natural extension of single variable techniques toseveral variables analysis and leads rapidly to important global results. Applications focus on global extension problems for CR functions, such as the Hartogs-Bochner phenomenon and removable singularities for CR functions. Threeappendices on differential manifolds, sheaf theory a nd functional analysis make the book self-contained. Each chapter begins with a detailed abstract, clearly demonstrating the structure and relations of following chapters. Newconcepts are clearly defined and theorems and propositions are proved in detail. Historical notes are also provided at the end of each chapter. Clear and succinct, this book will appeal to post-graduate students, young researchersseeking an introduction to holomorphic function theory in several variables and lecturers seeking a conci se book on the subject |
Note: | Springer eBooks |
Contents: | Elementary local properties of holomorphic functions of several complex variables |
Currents and complex structures | |
The Bochner | |
Martinelli | |
Koppelman kernel and formula applications | |
Extensions of CR functions | |
Extensions of holomorphic and CR functions on manifolds | |
Domains of holomorphy and pseudoconvexity | |
The Levi problem and the resolution of in strictly pseudoconvex domains | |
Characterisation of removable singularities of CR functions on a strictly pseudoconvex boundary | |
Appendices | |
ISBN: | 9780857290304 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differential equations, partial |
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Call number: | SPRINGER-2011-9780817682477:ONLINE Show nearby items on shelf |
Title: | The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator [electronic resource] |
Author(s): |
J. J Duistermaat |
Date: | 2011 |
Publisher: | Boston, MA : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Interest in the spin-c Dirac operator originally came about from the study of complex analytic manifolds, where in the non-Khler casethe Dolbeault operator is no longer suitable for getting local formulas for theRiemannRoch number or the holomorphic Lefschetz number. However, every symplectic manifold (phase space in classical mechanics) also carries an almost complex structure and hence a corresponding spin-c Dirac operator. Using the heatkernels theory of Berline, Getzler, and Vergne,this workrevis its some fundamental concepts of the theory, and presents the application to symplectic geometry. J.J. Duistermaat was well known for his beautiful and conciseexpositions of seemingly familiar concepts, and this classic studyis certainly no exception. Rep rinted as it was originally published,this workis as an affordable textthat will be of interest to a range of researchers ingeometric analysis and mathematical physics. Overall this is a carefully written, highly readable book on a very beautiful subject. Mathematical Reviews The book of J.J. Duistermaat is a nice introduction to analysis related[tothe]spin-c Dirac operator. ... The book is almost self contained, [is] readable, and will be useful for anybody who is interested in the topic. EMS Newsletter The author's book is a marvelous introduction to [these] objects andtheories. Zentralblatt MATH |
Note: | Springer eBooks |
Contents: | 1 Introduction |
2 The Dolbeault | |
Dirac Operator | |
3 Clifford Modules | |
4 The Spin Group and the Spin | |
c Group | |
5 The Spin | |
c Dirac Operator | |
6 Its Square | |
7 The Heat Kernel Method | |
8 The Heat Kernel Expansion | |
9 The Heat Kernel on a Principal Bundle | |
10 The Automorphism | |
11 The Hirzebruch | |
Riemann | |
Roch Integrand | |
12 The Local Lefschetz Fixed Point Formula | |
13 Characteristic Case | |
14 The Orbifold Version | |
15 Application to Symplectic Geometry | |
16 Appendix: Equivariant Forms | |
ISBN: | 9780817682477 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Modern Birkhuser Classics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Global analysis , Operator theory , Differential equations, partial , Global differential geometry |
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Call number: | SPRINGER-2010-9783764385149:ONLINE Show nearby items on shelf |
Title: | Pseudo-Differential Operators and Symmetries [electronic resource] : Background Analysis and Advanced Topics |
Author(s): |
Michael Ruzhansky Ville Turunen |
Date: | 2010 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This monograph develops a global quantization theory of pseudo-differential operators on compact Lie groups. Traditionally, the theory of pseudo-differential operators was introduced in the Euclidean setting with the aim oftackling a number of import ant problems in analysis and in the theory of partial differential equations. This also yields a local theory of pseudo-differential operators on manifolds. The present book takes a different approach byusing global symmetries of the space which are often available. First, a particular attention is paid to the theory of periodic operators, which are realized in the form of pseudo-differential and Fourier integral operators on thetorus. Then, the cases of the unitary group SU(2) and the 3-sphere are analyz ed in extensive detail. Finally, the monograph also develops elements of the theory of pseudo-differential operators on general compact Lie groups andhomogeneous spaces. The exposition of the book is self-contained and provides the reader with the backgro und material surrounding the theory and needed for working with pseudo-differential operators in different settings. Thebackground section of the book may be used for independent learning of different aspects of analysis and is complemented by numerous ex amples and exercises |
Note: | Springer eBooks |
Contents: | Preface |
Introduction | |
Part I Foundations of Analysis | |
A Sets, Topology and Metrics | |
B Elementary Functional Analysis | |
C Measure Theory and Integration | |
D Algebras | |
Part II Commutative Symmetries | |
1 Fourier Analysis on Rn | |
2 Pseudo | |
differential Operators on Rn | |
3 Periodic and Discrete Analysis | |
4 Pseudo | |
differential Operators on Tn | |
5 Commutator Characterisation of Pseudo | |
differential Operators | |
Part III Representation Theory of Compact Groups | |
6 Groups | |
7 Topological Groups | |
8 Linear Lie Groups | |
9 Hopf Algebras | |
Part IV Non | |
commutative Symmetries | |
10 Pseu | |
ISBN: | 9783764385149 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Pseudo-Differential Operators, Theory and Applications : v2 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups , Global analysis , Differential equations, partial |
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Call number: | SPRINGER-2010-9783034602136:ONLINE Show nearby items on shelf |
Title: | Mean Curvature Flow and Isoperimetric Inequalities [electronic resource] |
Author(s): |
Manuel Ritor Carlo Sinestrari |
Date: | 2010 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Geometric flows have many applications in physics and geometry. The mean curvature flow occurs in the description of the interface evolution in certain physical models. This is related to the property that such a flow is thegradient flow of the area functional and therefore appears naturally in problems where a surface energy is minimized. The mean curvature flow also has many geometric applications, in analogy with the Ricci flow of metrics on abstractriemannian manifolds. One can use this flow as a tool to obtain classification results for surfaces satisfying certain curvature conditions, as well as to construct minimal surfaces. Geometric flows, obtained from solutions ofgeometric parabolic equations, can be considered as an alternative tool to pr ove isoperimetric inequalities. On the other hand, isoperimetric inequalities can help in treating several aspects of convergence of these flows.Isoperimetric inequalities have many applications in other fields of geometry, like hyperbolic manifolds |
Note: | Springer eBooks |
Contents: | Formation of Singularities in the Mean Curvature Flow |
Geometry of hypersurfaces | |
Examples | |
Local existence and formation of singularities | |
Invariance properties | |
Singular behaviour of convex surfaces | |
Convexity estimates | |
Rescaling near a singularity | |
Huiskens monotonicity formula | |
Cylindrical and gradient estimates | |
Mean curvature flow with surgeries | |
Geometric Flows, Isoperimetric Inequalities and Hyperbolic Geometry | |
The classical isoperimetric inequality in Euclidean space | |
Surfaces | |
Higher dimensions | |
Some applications to hyperbolic geometry | |
ISBN: | 9783034602136 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Advanced Courses in Mathematics CRM Barcelona, Centre de Recerca Matemtica |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis , Global differential geometry |
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Call number: | SPRINGER-2010-9783034601764:ONLINE Show nearby items on shelf |
Title: | The Geometry of Filtering [electronic resource] |
Author(s): |
K. David Elworthy Yves Le Jan Xue-Mei Li |
Date: | 2010 |
Publisher: | Basel : Springer Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The geometry which is the topic of this book is that determined by a map of one space N onto another, M, mapping a diffusion process, or operator, on N to one on M. Filtering theory is the science of obtaining or estimatinginformation about a system from partial and possibly flawed observations of it. The system itself may be random, and the flaws in the observations can be caused by additional noise. In this volume the randomness and noises will be ofGaussian white noise type so that the system can be modelled by a diffusion process that is it evolves continuously in time in a Markovian way, the future evolution depending only on the present situation. This is the standardsituation of systems governed by Ito type stochastic differential equations. T he state space will be the smooth manifold, N, possibly infinite dimensional, and the observations will be obtained by a smooth map onto anothermanifold, N, say. We emphasise that the geometry is important even when both manifolds are Euclidean spaces. Th is can also be viewed from a purely partial differential equations viewpoint as one smooth second order elliptic partialdifferential operator lying above another, both with no zero order term. We consider the geometry of this situation with special emphas is on situations of geometric, stochastic analytic, or filtering interest. The most well studiedcase is of one Brownian motion being mapped to another with a consequent skew product decomposition (or equivalently the case of Riemannian submersions). This sort of decomposition is generalised and a key to the rest of the book. Itis used to study in particular, classical filtering, (semi-)connections determined by stochastic flows, and generalised Weitzenbock formulae |
Note: | Springer eBooks |
Contents: | 1 Diffusion Operators |
2 Decomposition of Diffusion Operators | |
3 Equivariant Diffusions on Principal Bundles | |
4 Projectible Diffusion Processes | |
5 Filtering with non | |
Markovian Observations | |
6 The Commutation Property | |
7 Example: Riemannian Submersions and Symmetric Spaces | |
8 Example: Stochastic Flows | |
9 Appendices | |
ISBN: | 9783034601764 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Frontiers in Mathematics, 1660-8046 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis , Global differential geometry , Distribution (Probability theory) |
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Call number: | SPRINGER-2010-9781441913432:ONLINE Show nearby items on shelf |
Title: | Around the Research of Vladimir Maz'ya II [electronic resource] : Partial Differential Equations |
Author(s): |
Ari Laptev |
Date: | 2010 |
Edition: | 1 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | International Mathematical Series Volume 12 Around the Research of Vladimir Maz'ya II Partial Differential Equations Edited by Ari Laptev Numerous influential contributions of Vladimir Maz'ya to PDEs are related to diverse areas.In particular, the fo llowing topics, close to the scientific interests of V. Maz'ya are discussed: semilinear elliptic equation with an exponential nonlinearity resolvents, eigenvalues, and eigenfunctions of elliptic operators inperturbed domains, homogenization, asymptotics for the Laplace-Dirichlet equation in a perturbed polygonal domain, the Navier-Stokes equation on Lipschitz domains in Riemannian manifolds, nondegenerate quasilinear subelliptic equationsof p-Laplacian type, singular perturbations of elliptic systems, el liptic inequalities on Riemannian manifolds, polynomial solutions to the Dirichlet problem, the first Neumann eigenvalues for a conformal class of Riemannian metrics,the boundary regularity for quasilinear equations, the problem on a steady flow over a tw o-dimensional obstacle, the well posedness and asymptotics for the Stokes equation, integral equations for harmonic single layer potential indomains with cusps, the Stokes equations in a convex polyhedron, periodic scattering problems, the Neumann problem for 4th order differential operators. Contributors include: Catherine Bandle (Switzerland), Vitaly Moroz (UK), andWolfgang Reichel (Germany) Gerassimos Barbatis (Greece), Victor I. Burenkov (Italy), and Pier Domenico Lamberti (Italy) Grigori Chechkin (Ru ssia) Monique Dauge (France), Sebastien Tordeux (France), and Gregory Vial (France) MartinDindos (UK) Andras Domokos (USA) and Juan J. Manfredi (USA) Yuri V. Egorov (France), Nicolas Meunier (France), and Evariste Sanchez-Palencia (France) Alexander Grigo r'yan (Germany) and Vladimir A. Kondratiev (Russia) DmitryKhavinson (USA) and Nikos Stylianopoulos (Cyprus) Gerasim Kokarev (UK) and Nikolai Nadirashvili (France) Vitali Liskevich (UK) and Igo |
Note: | Springer eBooks |
Contents: | Large Solutions to Semilinear Elliptic Equations with Hardy Potential and Exponential Nonlinearity |
Stability Estimates for Resolvents, Eigenvalues, and Eigenfunctions of Elliptic Operators on Variable Domains | |
Operator Pencil in a Domain with Concentrated Masses. A Scalar Analog of Linear Hydrodynamics | |
Selfsimilar Perturbation near a Corner: Matching Versus Multiscale Expansions for a Model Problem | |
Stationary Navier | |
Stokes Equation on Lipschitz Domains in Riemannian Manifolds with Nonvanishing Boundary Conditions | |
On the Regularity of Nonlinear Subelliptic Equations | |
Rigorous and | |
ISBN: | 9781441913432 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | International Mathematical Series, 1571-5485 : v12 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Functional analysis , Differential equations, partial |
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Call number: | SPRINGER-2010-9781441904348:ONLINE Show nearby items on shelf |
Title: | CR Submanifolds of Complex Projective Space [electronic resource] |
Author(s): |
Mirjana Djoric Masafumi Okumura |
Date: | 2010 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
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Note: | This book covers the necessary topics for learning the basic properties of complex manifolds and their submanifolds, offering an easy, friendly, and accessible introduction into the subject while aptly guiding the reader totopics of current research and to more advanced publications. The book begins with an introduction to the geometry of complex manifolds and their submanifolds and describes the properties of hypersurfaces and CR submanifolds, withparticular emphasis on CR submanifolds of maximal CR dimension. The second part contains results which are not new, but recently published in some mathematical journals. The final part contains several original results by the authors,with complete proofs. Key features of CR Submanifolds of Complex Projecti ve Space: - Presents recent developments and results in the study of submanifolds previously published only in research papers. - Special topics exploredinclude: the Khler manifold, submersion and immersion, codimension reduction of a submanifold, tubes o ver submanifolds, geometry of hypersurfaces and CR submanifolds of maximal CR dimension. - Provides relevant techniques, resultsand their applications, and presents insight into the motivations and ideas behind the theory. - Presents the fundamental defin itions and results necessary for reaching the frontiers of research in this field. This text is largelyself-contained. Prerequisites include basic knowledge of introductory manifold theory and of curvature properties of Riemannian geometry. Advanced under graduates, graduate students and researchers in differential geometry will benefitfrom this concise approach to an important topic |
Note: | Springer eBooks |
Contents: | 1. Complex manifold |
2. Almost complex structure | |
3. Complex vector space complexification | |
4. Khler manifold | |
5. Structure equations of a submanifold | |
6. Submanifolds of a Euclidean space | |
7. Submanifolds of a complex manifold | |
8. The Levi form | |
9. The principal circle bundle S^{2n+1}({\bf P}^n({\bf C}),S^1) | |
10. Submersion and immersion | |
11. Hypersurfaces of a Riemannian manifold of constant curvature | |
12. Hypersurfaces of a sphere S^{n+1}(1/a) | |
13. Hypersurfaces of a sphere with parallel shape operator | |
14. Codimension reduction of a submanifold | |
15. CR submani | |
ISBN: | 9781441904348 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Developments in Mathematics, Diophantine Approximation: Festschrift for Wolfgang Schmidt, 1389-2177 : v19 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis , Differential equations, partial , Global differential geometry |
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Title: | Modern Differential Geometry in Gauge Theories [electronic resource] : YangMills Fields, Volume II |
Author(s): |
Anastasios Mallios |
Date: | 2010 |
Edition: | 1 |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
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Note: | Differential geometry, in the classical sense, is developed through the theory of smooth manifolds. Modern differential geometry from the authors perspective is used in this work to describe physical theories of a geometriccharacter without using any notion of calculus (smoothness). Instead, an axiomatic treatment of differential geometry is presented via sheaf theory (geometry) and sheaf cohomology (analysis). Using vector sheaves, in place of bundles,based on arbitrary topological spaces, this uniq ue approach in general furthers new perspectives and calculations that generate unexpected potential applications. Modern Differential Geometry in Gauge Theories is a two-volume researchmonograph that systematically applies a sheaf-theoretic approach to s uch physical theories as gauge theory. Beginning with Volume 1, the focus is on Maxwell fields. All the basic concepts of this mathematical approach are formulatedand used thereafter to describe elementary particles, electromagnetism, and geometric prequa ntization. Maxwell fields are fully examined and classified in the language of sheaf theory and sheaf cohomology. Continuing in Volume 2, thissheaf-theoretic approach is applied to YangMills fields in general. The text contains a wealth of detailed and ri gorous computations and will appeal to mathematicians and physicists, along with advanced undergraduate and graduatestudents, interested in applications of differential geometry to physical theories such as general relativity, elementary particle physics and quantum gravity |
Note: | Springer eBooks |
Contents: | YangMills Theory:General Theory |
Abstract YangMills Theory | |
Moduli Spaces of | |
Connections of YangMills Fields | |
Geometry of YangMills | |
Connections | |
General Relativity | |
General Relativity, as a Gauge Theory. Singularities | |
ISBN: | 9780817646349 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Field theory (Physics) , Global analysis , Global differential geometry , Mathematical physics , Quantum theory |
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Call number: | SPRINGER-2010-9780387877129:ONLINE Show nearby items on shelf |
Title: | Von Karman Evolution Equations [electronic resource] : Well-posedness and Long Time Dynamics |
Author(s): |
Igor Chueshov Irena Lasiecka |
Date: | 2010 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The main goal of this book is to discuss and present results on well-posedness, regularity and long-time behavior of non-linear dynamic plate (shell) models described by von Karman evolutions. While many of the results presentedhere are the outgrowth of very recent studies by the authors, including a number of new original results here in print for the first time authors have provided a comprehensive and reasonably self-contained exposition of the generaltopic outlined above. This includes supplying all the functional analytic framework along with the function space theory as pertinent in the study of nonlinear plate models and more generally second order in time abstract evolutionequations. While von Karman evolutions are the object under considerat ions, the methods developed transcendent this specific model and may be applied to many other equations, systems which exhibit similar hyperbolic or ultra-hyperbolicbehavior (e.g. Berger's plate equations, Mindlin-Timoschenko systems, Kirchhoff-Boussinesq equations etc). In order to achieve a reasonable level of generality, the theoretical tools presented in the book are fairly abstract and tunedto general classes of second-order (in time) evolution equations, which are defined on abstract Banach spaces. The mathematical machinery needed to establish well-posedness of these dynamical systems, their regularity and long-timebehavior is developed at the abstract level, where the needed hypotheses are axiomatized. This approach allows to look at von Karman ev olutions as just one of the examples of a much broader class of evolutions. The generality of theapproach and techniques developed are applicable (as shown in the book) to many other dynamics sharing certain rather general properties. Extensive background material provided in the monograph and self-contained presentation make thisbook suitable as a graduate textbook |
Note: | Springer eBooks |
Contents: | Well |
Posedness | |
Preliminaries | |
Evolutionary Equations | |
Von Karman Models with Rotational Forces | |
Von Karman Equations Without Rotational Inertia | |
Thermoelastic Plates | |
Structural Acoustic Problems and Plates in a Potential Flow of Gas | |
Long | |
Time Dynamics | |
Attractors for Evolutionary Equations | |
Long | |
Time Behavior of Second | |
Order Abstract Equations | |
Plates with Internal Damping | |
Plates with Boundary Damping | |
Thermoelasticity | |
Composite WavePlate Systems | |
Inertial Manifolds for von Karman Plate Equations | |
ISBN: | 9780387877129 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Monographs in Mathematics, 1439-7382 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Differentiable dynamical systems , Differential equations, partial |
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Call number: | SPRINGER-2009-9783764399009:ONLINE Show nearby items on shelf |
Title: | Families of Conformally Covariant Differential Operators, Q-Curvature and Holography [electronic resource] |
Author(s): |
Andreas Juhl |
Date: | 2009 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The central object of the book is a subtle scalar Riemannian curvature quantity in even dimensions which is called Bransons Q-curvature. It was introduced by Thomas Branson about 15 years ago in connection with an attempt tosystematise the structure of conformal anomalies of determinants of conformally covariant differential operators on Riemannian manifolds. Since then, numerous relations of Q-curvature to other subjects have been discovered, and thecomprehension of its geometric significance in fou r dimensions was substantially enhanced through the studies of higher analogues of the Yamabe problem. The book attempts to reveal some of the structural properties of Q-curvature ingeneral dimensions. This is achieved by the development of a new framewor k for such studies. One of the main properties of Q-curvature is that its transformation law under conformal changes of the metric is governed by a remarkablelinear differential operator: a conformally covariant higher order generalization of the conforma l Laplacian. In the new approach, these operators and the associated Q-curvatures are regarded as derived quantities of certainconformally covariant families of differential operators which are naturally associated to hypersurfaces in Riemannian manifolds . This method is at the cutting edge of several central developments in conformal differential geometry inthe last two decades such as Fefferman-Graham ambient metrics, spectral theory on Poincar-Einstein spaces, tractor calculus, and Cartan geometry. In addition, the present theory is strongly inspired by the realization of the idea ofholography in the AdS/CFT-duality. This motivates the term holographic descriptions of Q-curvature |
Note: | Springer eBooks |
Contents: | Spaces, Actions, Representations and Curvature |
Conformally Covariant Powers of the Laplacian, Q | |
curvature and Scattering Theory | |
Paneitz Operator and Paneitz Curvature | |
Intertwining Families | |
Conformally Covariant Families | |
ISBN: | 9783764399009 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v275 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups , Global analysis , Global differential geometry , Mathematical physics |
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Location: | ONLINE |
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