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SPIRES-BOOKS: FIND KEYWORD GLOBAL ANALYSIS AND ANALYSIS ON MANIFOLDS *END*INIT* use /tmp/qspiwww.webspi1/7973.521 QRY 131.225.70.96 . find keyword global analysis and analysis on manifolds ( in books using www Cover
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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
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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
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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
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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
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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
Note:Springer 2013 e-book collections
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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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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Call number:SPRINGER-2010-9780817646349:ONLINE Show nearby items on shelf
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
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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
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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
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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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