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SPIRES-BOOKS: FIND KEYWORD GLOBAL DIFFERENTIAL GEOMETRY *END*INIT* use /tmp/qspiwww.webspi1/7979.157 QRY 131.225.70.96 . find keyword global differential geometry ( in books using www Cover
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Call number:9783319475127:ONLINE Show nearby items on shelf
Title:Pseudo-Differential Operators: Groups, Geometry and Applications
Author(s):
Date:2017
Size:1 online resource (VIII, 239 p. 23 illus., 11 illus. in color p.)
Contents:Pseudo-Differential Operators on the Affine Group -- Pseudo-Differential Operators on Non-Isotropic Heisenberg Groups with Multi-Dimensional Center -- Curvatures of the Heisenberg Group -- Ellipticity with Global Projection Conditions
-- Multilinear Localization Operators Associated to Quaternion Fourier Transforms -- A Time-Frequency Relationship between the Langevin Equation and the Harmonic Oscillator -- Are There Quantum Operators and Wave Functions in Standard
Probability Theory -- A Class of Non-Markovian Pseudo-Differential Operators of Lévy Type -- On the Solvability of Some Systems of Integro-Differential Equations with Anomalous Diffusion -- Visualizing Discrete Complex-Valued
Time-Frequency Representations -- The Reassigned Spectrogram of the Stockwell transform -- Continuous Multi-Wavelet Transforms for Blind Signal Separation.
ISBN:9783319475127
Series:eBooks
Series:Springer eBooks
Series:Springer 2017 package
Keywords: Mathematics , Operator theory , Partial differential equations , Information theory , Differential geometry , Probabilities , Mathematics , Operator Theory , Partial Differential Equations , Differential Geometry , Probability Theory and Stochastic Processes , Information and Communication, Circuits
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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-2016-9783319313382: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-2016-9783319243375: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-2014-9783642553615:ONLINE Show nearby items on shelf
Title:Algebra, Geometry and Mathematical Physics [electronic resource] : AGMP, Mulhouse, France, October 2011
Author(s): Abdenacer Makhlouf
Eugen Paal
Sergei D Silvestrov
Alexander Stolin
Date:2014
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:This book collects the proceedings of the Algebra, Geometry and Mathematical Physics Conference, held at the University of Haute Alsace, France, October 2011. Organized in the four areas of algebra, geometry, dynamical symmetriesand conservation laws and mathematical physics and applications, the book covers deformation theory and quantization Hom-algebras and n-ary algebraic structures Hopf algebra, integrable systems and related math structures jet theoryand Weil bundles Lie theory and applications non-commutative and Lie algebra and more. The papers explore the interplay between research in contemporary mathematics and physics concerned with generalizations of the main structures ofLie theory aimed at quantization, and discrete and non-commutative extensions of differential calculus and geometry, non-associative structures, actions of groups and semi-groups, non-commutative dynamics, non-commutative geometry andapplications in physics and beyond. The book benefits a broad audience of researchers a nd advanced students
Contents:Part I Algebra
Part II Geometry
Part III Dynamical Symmetries and Conservation Laws
Part IV Mathematical Physics and Applications
ISBN:9783642553615
Series:eBooks
Series:SpringerLink
Series:Springer Proceedings in Mathematics & Statistics, 2194-1009 : v85
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Topological Groups , Global differential geometry , Engineering mathematics
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Call number:SPRINGER-2014-9783642543012:ONLINE Show nearby items on shelf
Title:Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data [electronic resource]
Author(s): Carl-Fredrik Westin
Anna Vilanova
Bernhard Burgeth
Date:2014
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:Arising from the fourth Dagstuhl conference entitled Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data (2011), this book offers a broad and vivid view of current work in this emergingfield. Topics covered rang e from applications of the analysis of tensor fields to research on their mathematical and analytical properties. Part I, Tensor Data Visualization, surveys techniques for visualization of tensors and tensorfields in engineering, discusses the current sta te of the art and challenges, and examines tensor invariants and glyph design, including an overview of common glyphs. The second Part, Representation and Processing of Higher-orderDescriptors, describes a matrix representation of local phase, outlines ma thematical morphological operations techniques, extended for use in vector images, and generalizes erosion to the space of diffusion weighted MRI. Part III,Higher Order Tensors and Riemannian-Finsler Geometry, offers powerful mathematical language to mode l and analyze large and complex diffusion data such as High Angular Resolution Diffusion Imaging (HARDI) and Diffusion Kurtosis Imaging(DKI). A Part entitled Tensor Signal Processing presents new methods for processing tensor-valued data, including a nove l perspective on performing voxel-wise morphometry of diffusion tensor data using kernel-based approach, exploresthe free-water diffusion model, and reviews proposed approaches for computing fabric tensors, emphasizing trabecular bone research. The last P art, Applications of Tensor Processing, discusses metric and curvature tensors, two of themost studied tensors in geometry processing. Also covered is a technique for diagnostic prediction of first-episode schizophrenia patients based on brain diffusion M RI data. The last chapter presents an interactive system integratingthe visual analysis of diffusion MRI tractography with data from electroencephalography
Contents:Part I: Tensor Data Visualization: Top Challenges in the Visualization of Engineering Tensor Fields: M Hlawitschka et al
Tensor Invariants and Glyph Design: A. Kratz et al
Part II: Representation and Processing of Higher
order Descriptors: Monomial Phase: A Matrix Representation of Local Phase: H. Knutsson et al
Order Based Morphology for Colour Images via Matrix Fields: B. Burgeth et al
Sharpening Fibers in Diffusion Weighted MRI via Erosion: T.C.J. Dela Haije et al
Part III: Higher Order Tensors and Riemannian
Finsler Geometry: Higher
Order Tensors in Diffusion Imaging: Th
ISBN:9783642543012
Series:eBooks
Series:SpringerLink
Series:Mathematics and Visualization, 1612-3786
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer vision , Computer graphics , Differential equations, partial , Visualization , Global differential geometry
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Call number:SPRINGER-2014-9783642401572:ONLINE Show nearby items on shelf
Title:Progress in Mathematical Relativity, Gravitation and Cosmology [electronic resource] : Proceedings of the Spanish Relativity Meeting ERE2012, University of Minho, Guimares, Portugal, September 3-7, 2012
Author(s): Alfonso Garca-Parrado
Filipe C Mena
Filipe Moura
Estelita Vaz
Date:2014
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:This book contains contributions from the Spanish Relativity Meeting, ERE 2012, held in Guimares, Portugal, September 2012. It features more than 70 papers on a range of topics in general relativity and gravitation, frommathematical cosmology, numeri cal relativity and black holes to string theory and quantum gravity. Under the title Progress in Mathematical Relativity, Gravitation and Cosmology, ERE 2012 was attended by an exceptionalinternational list of over a hundred participants from the five con tinents and over forty countries. ERE is organized every year by one of the Spanish or Portuguese groups working in this area and is supported by the Spanish Society ofGravitation and Relativity (SEGRE). This book will be of interest to researchers in mat hematics and physics
Contents:Part I Plenary sessions
Part II Parallel sessions
Part III Poster presentations
ISBN:9783642401572
Series:eBooks
Series:SpringerLink
Series:Springer Proceedings in Mathematics & Statistics, 2194-1009 : v60
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis , Global differential geometry , Mathematical physics
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Call number:SPRINGER-2014-9783642315435:ONLINE Show nearby items on shelf
Title:An Introduction to Compactness Results in Symplectic Field Theory [electronic resource]
Author(s): Casim Abbas
Date:2014
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:This book provides an introduction to symplectic field theory, a new and important subject which is currently being developed. The starting point of this theory are compactness results for holomorphic curves established in thelast decade. The author presents a systematic introduction providing a lot of background material, much of which is scattered throughout the literature. Since the content grew out of lectures given by the author, the main aim is toprovide an entry point into symplectic field the ory for non-specialists and for graduate students. Extensions of certain compactness results, which are believed to be true by the specialists but have not yet been published in theliterature in detail, top off the scope of this monograph
ISBN:9783642315435
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global differential geometry , Cell aggregation Mathematics
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Call number:SPRINGER-2014-9783319086903:ONLINE Show nearby items on shelf
Title:Control of Nonholonomic Systems: from Sub-Riemannian Geometry to Motion Planning [electronic resource]
Author(s): Frdric Jean
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:Nonholonomic systems are control systems which depend linearly on the control. Their underlying geometry is the sub-Riemannian geometry, which plays for these systems the same role as Euclidean geometry does for linear systems. Inparticular the usual notions of approximations at the first order, that are essential for control purposes, have to be defined in terms of this geometry. The aim of these notes is to present these notions of approximation and theirapplication to the motion planning problem f or nonholonomic systems
Contents:1Geometry of nonholonomic systems
2First
order theory
3Nonholonomic motion planning
4 Appendix A:Composition of flows of vector fields
5Appendix B: The different systems of privileged coordinates
ISBN:9783319086903
Series:eBooks
Series:SpringerLink
Series:SpringerBriefs in Mathematics, 2191-8198
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer science , Artificial intelligence , Systems theory , Global differential geometry
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Call number:SPRINGER-2014-9783319086668:ONLINE Show nearby items on shelf
Title:An Introduction to Riemannian Geometry [electronic resource] : With Applications to Mechanics and Relativity
Author(s): Leonor Godinho
Jos Natrio
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:Unlike many other texts on differential geometry, this textbook also offers interesting applications to geometric mechanics and general relativity. The first part is a concise and self-contained introduction to the basics ofmanifolds, differential fo rms, metrics and curvature. The second part studies applications to mechanics and relativity including the proofs of the Hawking and Penrose singularity theorems. It can be independently used for one-semestercourses in either of these subjects. The main i deas are illustrated and further developed by numerous examples and over 300 exercises. Detailed solutions are provided for many of these exercises, making An Introduction to RiemannianGeometry ideal for self-study
Contents:Differentiable Manifolds
Differential Forms
Riemannian Manifolds
Curvature
Geometric Mechanics
Relativity
ISBN:9783319086668
Series:eBooks
Series:SpringerLink
Series:Universitext, 0172-5939
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global differential geometry , Mechanics
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Call number:SPRINGER-2014-9783319070346:ONLINE Show nearby items on shelf
Title:Differential Characters [electronic resource]
Author(s): Christian Br
Christian Becker
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:Providing a systematic introduction to differential characters as introduced by Cheeger and Simons, this text describes important concepts such as fiber integration, higher dimensional holonomy, transgression, and the productstructure in a geometric manner. Differential characters form a model of what is nowadays called differential cohomology, which is the mathematical structure behind the higher gauge theories in physics.
Contents:Differential Characters and Geometric Chains
Relative differential Cohomology
Index
ISBN:9783319070346
Series:eBooks
Series:SpringerLink
Series:Lecture Notes in Mathematics, 0075-8434 : v2112
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global differential geometry , Algebraic topology
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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-2014-9783319062488:ONLINE Show nearby items on shelf
Title:Geometric Methods in Physics [electronic resource] : XXXII Workshop, Biaowiea, Poland, June 30-July 6, 2013
Author(s): Piotr Kielanowski
Pierre Bieliavsky
Alexander Odesskii
Anatol Odzijewicz
Martin Schlichenmaier
Theodore Voronov
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Birkhuser
Size:1 online resource
Note:The Biaowiea Workshops on Geometric Methods in Physics, which are hosted in the unique setting of the Biaowiea natural forest in Poland, are among the most important meetings in the field. Every year some 80 to 100participants from both the mathemati cs and physics world join to discuss new developments and to exchange ideas. The current volume was produced on the occasion of the 32nd meeting in 2013. It is now becoming a tradition that theWorkshop is followed by a School on Geometry and Physics, whic h consists of advanced lectures for graduate students and young researchers. Selected speakers at the 2013 Workshop were asked to contribute to this book, and their work wassupplemented by additional review articles. The selection shows that, despite its now long tradition, the workshop remains at the cutting edge of research. The 2013 Workshop also celebrated the 75th birthday of Daniel Sternheimer, andon this occasion the discussion mainly focused on his contributions to mathematical physics such as def ormation quantization, Poisson geometry, symplectic geometry and non-commutative differential geometry
Contents:Preface
Part I: Deformation, Quantization: Scientific Landmarks of Daniel Sternheimer
Part II: Quantum Mechanics
Part III: Groups and Non
commutative Structures
Part IV: Differential Equations and Special Functions
Part V: General Methods
ISBN:9783319062488
Series:eBooks
Series:SpringerLink
Series:Trends in Mathematics, 2297-0215
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Group theory , Global analysis
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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-2014-9783319048048:ONLINE Show nearby items on shelf
Title:Sub-Riemannian Geometry and Optimal Transport [electronic resource]
Author(s): Ludovic Rifford
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:Thebook provides an introduction to sub-Riemannian geometry and optimal transport and presents some of the recent progress in these two fields. The text is completely self-contained: the linear discussion, containing all theproofs of the stated resul ts, leads the reader step by step from the notion of distribution at the very beginning to the existence of optimal transport maps for Lipschitz sub-Riemannian structure.The combination of geometry presentedfrom an analytic point of view and of optimal tr ansport, makes the book interesting for a very large community. This set of notes grew from a series of lectures given by the author during a CIMPA school in Beirut, Lebanon
Contents:1 Sub
Riemannian structures
2 Sub
Riemannian geodesics
3 Introduction to optimal transport
Appendix AOrdinary differential equations
Appendix BElements of differential calculus
References
ISBN:9783319048048
Series:eBooks
Series:SpringerLink
Series:SpringerBriefs in Mathematics, 2191-8198
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Systems theory , Global differential geometry , Mathematical optimization
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Call number:SPRINGER-2014-9783319046754:ONLINE Show nearby items on shelf
Title:Geometry and its Applications [electronic resource]
Author(s): Vladimir Rovenski
Pawe Walczak
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:This volume has been divided into two parts: Geometry and Applications. The geometry portion of the book relates primarily to geometric flows, laminations, integral formulae, geometry of vector fields on Lie groups, andosculation the articles in the applications portion concern some particular problems of the theory of dynamical systems, including mathematical problems of liquid flows and a study of cycles for non-dynamical systems. This Work isbased on the second international workshop entitled Geom etry and Symbolic Computations, held on May 15-18, 2013 at the University of Haifa and is dedicated to modeling (using symbolic calculations) in differential geometry and itsapplications in fields such as computer science, tomography, and mechanics. It is intended to create a forum for students and researchers in pure and applied geometry to promote discussion of modern state-of-the-art in geometricmodeling using symbolic programs such as Maple and Mathematica, as well as presentation of new results.
Contents:Part I: Geometry
The Ricci flow on some generalized Wallach spaces (N.A. Abiev, A. Arvanitoyeorgos, Y.G. Nikonorov, P. Siasos)
Gaussian mean curvature flow for submanifolds in space forms (A. Borisenko, V. Rovenski)
Cantor laminationsand exceptional minimal sets in codimension one foliations(G. Hector)
Integral formulas in foliations theory (K. Andrzejewski, P. Walczak, V. Rovenski)
On prescribing the mixed scalar curvature of a foliations (V. Rovenski, L. Zelenko)
The partial Ricci flow for foliations (V. Rovenski)
Osculation in general (P. Walczak)
On stability of
ISBN:9783319046754
Series:eBooks
Series:SpringerLink
Series:Springer Proceedings in Mathematics & Statistics, 2194-1009 : v72
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global differential geometry
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Call number:SPRINGER-2014-9783319024417:ONLINE Show nearby items on shelf
Title:Cohomological Aspects in Complex Non-Khler Geometry [electronic resource]
Author(s): Daniele Angella
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:In these notes, we provide a summary of recentresults on the cohomological properties of compact complex manifolds not endowed with a Khler structure. On the one hand, the large number of developed analytic techniques makes itpossible to prove strong cohomological properties for compact Khler manifolds. On the other, in order to further investigate any of these properties, it is natural to look for manifolds that do not have any Khler structure. Wefocus in particular on studying Bott-Chern and Aeppli cohomologies of compact complex manifolds. Several results concerning the computations of Dolbeault and Bott-Chern cohomologies on nilmanifolds are summarized, allowing readers tostudy explicit examples. Manifolds endowed with almost-complex structures, or with other special structures (such as, for example, symplectic, generalized-complex, etc.), are also considered
Contents:Preliminaries on (almost
) complex manifolds
Cohomology of complex manifolds
Cohomology of nilmanifolds
Cohomology of almost
complex manifolds
References
ISBN:9783319024417
Series:eBooks
Series:SpringerLink
Series:Lecture Notes in Mathematics, 0075-8434 : v2095
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differential equations, partial , Global differential geometry
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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-2014-9783319020877:ONLINE Show nearby items on shelf
Title:An Invitation to Hypoelliptic Operators and Hrmander's Vector Fields [electronic resource]
Author(s): Marco Bramanti
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:Hrmander's operators are an important class of linear elliptic-parabolic degenerate partial differential operators with smooth coefficients, which have been intensively studied since the late 1960s and are still an active fieldof research. This text provides the reader with a general overview of the field, with its motivations and problems, some of its fundamental results, and some recent lines of development
Contents:1 Hrmander's operators: what they are
2 Hrmander's operators: why they are studied
3 A priori estimates in Sobolev spaces
4 Geometry of Hrmander's vector fields
5 Beyond Hrmander's operators
ISBN:9783319020877
Series:eBooks
Series:SpringerLink
Series:SpringerBriefs in Mathematics, 2191-8198
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Operator theory , Differential equations, partial
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Call number:SPRINGER-2014-9783319017365:ONLINE Show nearby items on shelf
Title:A Differential Approach to Geometry [electronic resource] : Geometric Trilogy III
Author(s): Francis Borceux
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:This book presents the classical theory of curves in the plane and three-dimensional space, and the classical theory of surfaces in three-dimensional space. It pays particular attention to the historical development of the theoryand the preliminary a pproaches that support contemporary geometrical notions. It includes a chapter that lists a very wide scope of plane curves and their properties. The book approaches the threshold of algebraic topology, providingan integrated presentation fully accessible to undergraduate-level students. At the end of the 17th century, Newton and Leibniz developed differential calculus, thus making available the very wide range of differentiable functions,not just those constructed from polynomials. During the 18th centu ry, Euler applied these ideas to establish what is still today the classical theory of most general curves and surfaces, largely used in engineering. Enter thisfascinating world through amazing theorems and a wide supply of surprising examples. Reach the doors of algebraic topology by discovering just how an integer (= the Euler-Poincar characteristics) associated with a surface gives you alot of interesting information on the shape of the surface. And penetrate the intriguing world of Riemannian geometry , the geometry that underlies the theory of relativity. The book is of interest to all those who teach classicaldifferential geometry up to quite an advanced level. The chapter on Riemannian geometry is of great interest to those who have to intuitively introduce students to the highly technical nature of this branch of mathematics, inparticular when preparing students for courses on relativity
Contents:Introduction
Preface
1.The Genesis of Differential Methods
2.Plane Curves
3.A Museum of Curves
4.Skew Curves
5.Local Theory of Surfaces
6.Towards Riemannian Geometry
7.Elements of Global Theory of Surfaces
Appendices: A.Topology
B.Differential Equations
Index
Bibliography
ISBN:9783319017365
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry , Global differential geometry
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Call number:SPRINGER-2014-9783319002279:ONLINE Show nearby items on shelf
Title:Analysis and Geometry of Markov Diffusion Operators [electronic resource]
Author(s): Dominique Bakry
Ivan Gentil
Michel Ledoux
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:The present volume is an extensive monograph on the analytic and geometric aspects of Markov diffusion operators. It focuses on the geometric curvature properties of the underlying structure in order to study convergence toequilibrium, spectral bound s, functional inequalities such as Poincar, Sobolev or logarithmic Sobolev inequalities, and various bounds on solutions of evolution equations. At the same time, it covers a large class of evolution andpartial differential equations. The book is intended to serve as an introduction to the subject and to be accessible for beginning and advanced scientists and non-specialists. Simultaneously, it covers a wide range of results andtechniques from the early developments in the mid-eighties to the latest achie vements. As such, students and researchers interested in the modern aspects of Markov diffusion operators and semigroups and their connections to analyticfunctional inequalities, probabilistic convergence to equilibrium and geometric curvature will find i t especially useful. Selected chapters can also be used for advanced courses on the topic
Contents:Introduction
Part I Markov semigroups, basics and examples: 1.Markov semigroups
2.Model examples
3.General setting
Part II Three model functional inequalities: 4.Poincar inequalities
5.Logarithmic Sobolev inequalities
6.Sobolev inequalities
Part III Related functional, isoperimetric and transportation inequalities: 7.Generalized functional inequalities
8.Capacity and isoperimetry
type inequalities
9.Optimal transportation and functional inequalities
Part IV Appendices: A.Semigroups of bounded operators on a Banach space
B.Elements of stochastic calculus
C
ISBN:9783319002279
Series:eBooks
Series:SpringerLink
Series:Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 0072-7830 : v348
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Functional analysis , Differential equations, partial , Global differential geometry , Distribution (Probability theory)
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Call number:SPRINGER-2014-9781447154969:ONLINE Show nearby items on shelf
Title:Morse Theory and Floer Homology [electronic resource]
Author(s): Michle Audin
Mihai Damian
Date:2014
Publisher:London : Springer London : Imprint: Springer
Size:1 online resource
Note:This book is an introduction to modern methods of symplectic topology. It is devoted to explaining the solution of an important problem originating from classical mechanics: the 'Arnold conjecture', which asserts that the numberof 1-periodic trajecto ries of a non-degenerate Hamiltonian system is bounded below by the dimension of the homology of the underlying manifold. The first part is a thorough introduction to Morse theory, a fundamental tool ofdifferential topology. It defines the Morse complex a nd the Morse homology, and develops some of their applications. Morse homology also serves a simple model for Floer homology, which is covered in the second part. Floer homology isan infinite-dimensional analogue of Morse homology. Its involvement has bee n crucial in the recent achievements in symplectic geometry and in particular in the proof of the Arnold conjecture. The building blocks of Floer homology aremore intricate and imply the use of more sophisticated analytical methods, all of which are expla ined in this second part. The three appendices present a few prerequisites in differential geometry, algebraic topology and analysis. Thebook originated in a graduate course given at Strasbourg University, and contains a large range of figures and exercis es. Morse Theory and Floer Homology will be particularly helpful for graduate and postgraduate students
Contents:Introduction to Part I
Morse Functions
Pseudo
Gradients
The Morse Complex
Morse Homology, Applications
Introduction to Part II
What You Need To Know About Symplectic Geometry
The Arnold Conjecture and the Floer Equation
The Maslov Index
Linearization and Transversality
Spaces of Trajectories
From Floer To Morse
Floer Homology: Invariance
Elliptic Regularity
Technical Lemmas
Exercises for the Second Part
Appendices: What You Need to Know to Read This Book
ISBN:9781447154969
Series:eBooks
Series:SpringerLink
Series:Universitext, 0172-5939
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry , Global differential geometry , Algebraic topology , Cell aggregation Mathematics
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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-2013-9788847028418:ONLINE Show nearby items on shelf
Title:Geometric Properties for Parabolic and Elliptic PDE's [electronic resource]
Author(s): Rolando Magnanini
Shigeru Sakaguchi
Angelo Alvino
Date:2013
Publisher:Milano : Springer Milan : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The study of qualitative aspects of PDE's has always attracted much attention from the early beginnings. More recently, once basic issues about PDE's, such as existence, uniqueness and stability of solutions, have been understoodquite well, research on topological and/or geometric properties of their solutions has become more intense. The study of these issues is attracting the interest of an increasing number of researchers and is now a broad andwell-established research area, with contributions tha t often come from experts from disparate areas of mathematics, such as differential and convex geometry, functional analysis, calculus of variations, mathematical physics, to name afew. This volume collects a selection of original results and informative surveys by a group of international specialists in the field, analyzes new trends and techniques and aims at promoting scientific collaboration and stimulatingfuture developments and perspectives in this very active area of research
Note:Springer eBooks
Contents:Goro Akagi, Stability and instability of group invariant asymptotic profiles for fast diffusion equations
Elvise Berchio, A family of Hardy
Rellich type inequalities involving the L2
norm of the Hessian matrices
Massimiliano Bianchini and Paolo Salani, Power concavity for solutions of nonlinear elliptic problems in convex domains
Lorenzo Brasco and Rolando Magnanini, The heart of a convex set
Giulio Ciraolo, A viscosity equation for minimizers of a class of very degenerate elliptic functionals
Adele Ferone, Kato's inequality in the half space: an alternative proof and relative i
ISBN:9788847028418
Series:e-books
Series:SpringerLink (Online service)
Series:Springer INdAM Series, 2281-518X : v2
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Functional analysis , Differential equations, partial , Discrete groups , Global differential geometry , Mathematical optimization
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Call number:SPRINGER-2013-9788847028357:ONLINE Show nearby items on shelf
Title:Spectral Theory and Quantum Mechanics [electronic resource] : With an Introduction to the Algebraic Formulation
Author(s): Valter Moretti
Date:2013
Publisher:Milano : Springer Milan : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book pursues the accurate study of the mathematical foundations of Quantum Theories. It may be considered an introductory text on linear functional analysis with a focus on Hilbert spaces. Specific attention is given tospectral theory features t hat are relevant in physics. Having left the physical phenomenology in the background, it is the formal and logical aspects of the theory that are privileged. Another not lesser purpose is to collect in oneplace a number of useful rigorous statements on t he mathematical structure of Quantum Mechanics, including some elementary, yet fundamental, results on the Algebraic Formulation of Quantum Theories. In the attempt to reach out toMaster's or PhD students, both in physics and mathematics, the material is designed to be self-contained: it includes a summary of point-set topology and abstract measure theory, together with an appendix on differential geometry. Thebook should benefit established researchers to organise and present the profusion of advanced ma terial disseminated in the literature. Most chapters are accompanied by exercises, many of which are solved explicitly
Note:Springer eBooks
Contents:Introduction and mathematical backgrounds
Normed and Banach spaces, examples and applications
Hilbert spaces and bounded operators
Families of compact operators on Hilbert spaces and fundamental properties
Densely
defined unbounded operators on Hilbert spaces
Phenomenology of quantum systems and Wave Mechanics: an overview
The first 4 axioms of QM: propositions, quantum states and observables
Spectral Theory I: generalities, abstract C
algebras and operators in B(H)
Spectral theory II: unbounded operators on Hilbert spaces
Spectral Theory III: applications
Mathem
ISBN:9788847028357
Series:e-books
Series:SpringerLink (Online service)
Series:UNITEXT, 2038-5714
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Mathematical physics
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Call number:SPRINGER-2013-9783642396267:ONLINE Show nearby items on shelf
Title:Constant Mean Curvature Surfaces with Boundary [electronic resource]
Author(s): Rafael Lpez
Date:2013
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The study of surfaces with constant mean curvature (CMC) is one of the main topics in classical differential geometry. Moreover, CMC surfaces are important mathematical models for the physics of interfaces in the absence ofgravity, where they separat e two different media, or for capillary phenomena. Further, as most techniques used in the theory of CMC surfaces not only involve geometric methods but also PDE and complex analysis, the theory is also ofgreat interest for many other mathematical fields. While minimal surfaces and CMC surfaces in general have already been treated in the literature, the present work is the first to present a comprehensive study of compact surfaceswith boundaries, narrowing its focus to a geometric view. Basic issues incl ude the discussion whether the symmetries of the curve inherit to the surface the possible values of the mean curvature, area and volume stability thecircular boundary case and the existence of the Plateau problem in the non-parametric case. The expositio n provides an outlook on recent research but also a set of techniques that allows the results to be expanded to other ambientspaces. Throughout the text, numerous illustrations clarify the results and their proofs. The book is intended for graduate stude nts and researchers in the field of differential geometry and especially theory of surfaces, includinggeometric analysis and geometric PDEs. It guides readers up to the state-of-the-art of the theory and introduces them to interesting open problems
Note:Springer eBooks
Contents:Introduction
Surfaces with Constant Mean Curvature
Constant Mean Curvature Embedded Surfaces
The Flux Formula for Constant Mean Curvature Surfaces
The Area and the Volume of a Constant Mean Curvature Surface
Constant Mean Curvature Discs with Circular Boundary
The Dirichlet Problem of the CMC Equation
The Dirichlet Problem in Unbounded Domains
Constant Mean Curvature Surfaces in Hyperbolic Space
The Dirichlet Problem in Hyperbolic Space
Constant Mean Curvature Surfaces in Lorentz
Minkowski Space
Appendix: A. The Variation Formula of the Area and the Volume
B
ISBN:9783642396267
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Monographs in Mathematics, 1439-7382
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differential equations, partial , Geometry , Global differential geometry
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Call number:SPRINGER-2013-9783642362163:ONLINE Show nearby items on shelf
Title:Clifford Algebras and Lie Theory [electronic resource]
Author(s): Eckhard Meinrenken
Date:2013
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
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Note:This monograph provides an introduction to the theory of Clifford algebras, with an emphasis on its connections with the theory of Lie groups and Lie algebras. The book starts with a detailed presentation of the main results onsymmetric bilinear form s and Clifford algebras. It develops the spin groups and the spin representation, culminating in Cartans famous triality automorphism for the group Spin(8). The discussion of enveloping algebras includes apresentation of Petraccis proof of the PoincarBirk hoffWitt theorem. This is followed by discussions of Weil algebras, Chern--Weil theory, the quantum Weil algebra, and the cubic Dirac operator. The applications to Lietheory include Duflos theorem for the case of quadratic Lie algebras, multiplets of rep resentations, and Dirac induction. The last part of the book is an account of Kostants structure theory of the Clifford algebra over asemisimple Lie algebra. It describes his Clifford algebra analogue of the HopfKoszulSamelson theorem, and explains his fa scinating conjecture relating the Harish-Chandra projection for Clifford algebras to the principalsl(2) subalgebra. Aside from these beautiful applications, the book will serve as a convenient and up-to-date reference for background material from Cliffor d theory, relevant for students and researchers in mathematics andphysics
Note:Springer eBooks
Contents:Preface
Conventions
List of Symbols
1 Symmetric bilinear forms
2 Clifford algebras
3 The spin representation
4 Covariant and contravariant spinors
5 Enveloping algebras
6 Weil algebras
7 Quantum Weil algebras
8 Applications to reductive Lie algebras
9 D(g k) as a geometric Dirac operator
10 The HopfKoszulSamelson Theorem
11 The Clifford algebra of a reductive Lie algebra
A Graded and filtered super spaces
B Reductive Lie algebras
C Background on Lie groups
References
Index
ISBN:9783642362163
Series:e-books
Series:SpringerLink (Online service)
Series:Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 0071-1136 : v58
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Topological Groups , Global differential geometry , Mathematical physics
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Call number:SPRINGER-2013-9783642310904:ONLINE Show nearby items on shelf
Title:Poisson Structures [electronic resource]
Author(s): Camille Laurent-Gengoux
Anne Pichereau
Pol Vanhaecke
Date:2013
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
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Note:Poisson structures appear in a large variety of contexts, ranging from string theory, classical/quantum mechanics and differential geometry to abstract algebra, algebraic geometry and representation theory. In each one of thesecontexts, it turns out that the Poisson structure is not a theoretical artifact, but a key element which, unsolicited, comes along with the problem that is investigated, and its delicate properties are decisive for the solution to theproblem in nearly all cases. Poisson Structu res is the first book that offers a comprehensive introduction to the theory, as well as an overview of the different aspects of Poisson structures.The first part coverssolid foundations,the central part consists of a detailed exposition of the different known types of Poisson structures and of the (usually mathematical) contexts in which they appear, and the final part is devoted to the two main applications ofPoisson structures (integrable systems and deformation quantization). The clear structure of th e book makes it adequate for readers who come across Poisson structures in their research or for graduate students or advanced researcherswhoare interested in anintroduction to the many facets and applications of Poisson structures
Note:Springer eBooks
Contents:Part I Theoretical Background:1.Poisson Structures: Basic Definitions
2.Poisson Structures: Basic Constructions
3.Multi
Derivations and Khler Forms
4.Poisson (Co)Homology
5.Reduction
Part II Examples:6.Constant Poisson Structures, Regular and Symplectic Manifolds
7.Linear Poisson Structures and Lie Algebras
8.Higher Degree Poisson Structures
9.Poisson Structures in Dimensions Two and Three
10.R
Brackets and r
Brackets
11.PoissonLie Groups
Part III Applications:12.Liouville Integrable Systems
13.Deformation Quantization
A Multilinear Algebra
B Real
ISBN:9783642310904
Series:e-books
Series:SpringerLink (Online service)
Series:Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 0072-7830 : v347
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Topological Groups , Global analysis (Mathematics) , Global differential geometry
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Call number:SPRINGER-2013-9783642309588:ONLINE Show nearby items on shelf
Title:Encyclopedia of Distances [electronic resource]
Author(s): Michel Marie Deza
Elena Deza
Date:2013
Edition:2nd ed. 2013
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This updated and revised second edition of the leading reference volume on distance metrics includes a wealth of new material that reflects advances in a field now regarded as an essential tool in many areas of pure and appliedmathematics. The publi cation of this volume coincides with intensifying research efforts into metric spaces and especially distance design for applications. Accurate metrics have become a crucial goal in computational biology, imageanalysis, speech recognition and information retrieval. Leaving aside the practical questions that arise during the selection of a good distance function, this work focuses on providing the research community with aninvaluable comprehensive listing of the main available distances. As well as provi ding standalone introductions and definitions, the encyclopedia facilitates swift cross-referencing with easily navigable bold-faced textual links tocore entries. In addition to distances themselves, the authors have collated numerous fascinating curiosit ies in their Whos Who of metrics, including distance-related notions and paradigms that enable applied mathematicians in othersectors to deploy research tools that non-specialists justly view as arcane. In expanding access to these techniques, and in many cases enriching the context of distances themselves, this peerless volume is certain to stimulate freshresearch
Note:Springer eBooks
Contents:Part I. Mathematics of Distances
1 General Definitions
2 Topological Spaces
3 Generalization of Metric Spaces
4 Metric Transforms
5 Metrics on Normed Structures
Part II. Geometry and Distances
6 Distances in Geometry
7 Riemannian and Hermitian Metrics
8 Distances on Surfaces and Knots
9 Distances on Convex Bodies, Cones and Simplicial Complexes
Part III. Distances in Classical Mathematics
10 Distances in Algebra
11 Distances on Strings and Permutations
12 Distances on Numbers, Polynominals and Matrices
13 Distances in Functional Analysis
14 Dista
ISBN:9783642309588
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer science Mathematics , Visualization , Geometry , Global differential geometry , Topology , Engineering mathematics
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Call number:SPRINGER-2013-9783319008196:ONLINE Show nearby items on shelf
Title:An Introduction to the Khler-Ricci Flow [electronic resource]
Author(s): Sebastien Boucksom
Philippe Eyssidieux
Vincent Guedj
Date:2013
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
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Note:This volume collects lecture notes from courses offered at several conferences and workshops, and provides the first exposition in book form of the basic theory of the Khler-Ricci flow and its current state-of-the-art. Whileseveral excellent books on Khler-Einstein geometry are available, there have been no such works on the Khler-Ricci flow. The book will serve as a valuable resource for graduate students and researchers in complex differentialgeometry, complex algebraic geometry and Riemannian geom etry, and will hopefully foster further developments in this fascinating area of research. The Ricci flow was first introduced by R. Hamilton in the early 1980s, and is centralin G. Perelmans celebrated proof of the Poincar conjecture. When specialized f or Khler manifolds, it becomes the Khler-Ricci flow, and reduces to a scalar PDE (parabolic complex Monge-Ampre equation). As a spin-off of hisbreakthrough, G. Perelman proved the convergence of the Khler-Ricci flow on Khler-Einstein manifolds of positive scalar curvature (Fano manifolds). Shortly after, G. Tian and J. Song discovered a complex analogue of Perelmansideas: the Khler-Ricci flow is a metric embodiment of the Minimal Model Program of the underlying manifold, and flips and divisorial contracti ons assume the role of Perelmans surgeries
Note:Springer eBooks
Contents:The (real) theory of fully non linear parabolic equations
The KRF on positive Kodaira dimension Khler manifolds
The normalized Khler
Ricci flow on Fano manifolds
Bibliography
ISBN:9783319008196
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v2086
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differential equations, partial , Global differential geometry
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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
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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-2013-9783034805728:ONLINE Show nearby items on shelf
Title:Offbeat Integral Geometry on Symmetric Spaces [electronic resource]
Author(s): Valery V Volchkov
Vitaly V Volchkov
Date:2013
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
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Note:Springer 2013 e-book collections
Note:The book demonstrates the development of integral geometry on domains of homogeneous spaces since 1990. It covers a wide range of topics, including analysis on multidimensional Euclidean domains and Riemannian symmetric spaces ofarbitrary ranks as we ll as recent work on phase space and the Heisenberg group. The book includes many significant recent results, some of them hitherto unpublished, among which can be pointed out uniqueness theorems for variousclasses of functions, far-reaching generalizatio ns of the two-radii problem, the modern versions of the Pompeiu problem, and explicit reconstruction formulae in problems of integral geometry. These results are intriguing and useful invarious fields of contemporary mathematics. The proofs given are mini mal in the sense that they involve only those concepts and facts which are indispensable for the essence of the subject. Each chapter provides a historicalperspective on the results presented and includes many interesting open problems. Readers will find this book relevant to harmonic analysis on homogeneous spaces, invariant spaces theory, integral transforms on symmetric spaces and theHeisenberg group, integral equations, special functions, and transmutation operators theory
Note:Springer eBooks
Contents:Preface
Part 1. Analysis on Symmetric Spaces. 1 Preliminaries
2 The Euclidean case
3 Symmetric spaces of the non
compact type
4 Analogies for compact two
point homogeneous Spaces
5 The phase space associated to the Heisenberg group
Part 2. Offbeat Integral Geometry
1 Functions with zero ball means on Euclidean space
2 Two
radii theorems in symmetric spaces
3 The problem of finding a function from its ball means
4 Sets with the Pompeiu property
5 Functions with zero integrals over polytopes
6 Ellipsoidal means
7 The Pompeiu property on a sphere
8 The Pompeiu
ISBN:9783034805728
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Harmonic analysis , Integral Transforms , Functions, special , Global differential geometry
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Call number:SPRINGER-2013-9783034805346:ONLINE Show nearby items on shelf
Title:Developments of Harmonic Maps, Wave Maps and Yang-Mills Fields into Biharmonic Maps, Biwave Maps and Bi-Yang-Mills Fields [electronic resource]
Author(s): Yuan-Jen Chiang
Date:2013
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Harmonic maps between Riemannian manifolds were first established in 1964. Wave maps are harmonic maps on Minkowski spaces and have been studied since the 1990s. Yang-Mills fields, the critical points of Yang-Mills functionals ofconnections whose cur vature tensors are harmonic, were explored by a few physicists in the 1950s, and biharmonic maps (generalizing harmonic maps) were introducedin 1986. The book presents an overview of the important developmentsmadein these fields since they first came up. Furthermore,it introduces biwave maps (generalizing wave maps) which were first studiedin 2009, and bi-Yang-Mills fields (generalizing Yang-Mills fields) first investigated in 2008.Other topicsdiscussed are exponential harmonic maps, exponential wave maps and exponential Yang-Mills fields
Note:Springer eBooks
Contents:Preface. 1 Harmonic Maps
2 Wave Maps
3 Yang
Mills Fields
4 Biharmonic Maps
5 Biwave Maps
6 Bi
Yang
Mills Fields
7 Exponential Harmonic Maps
8 Exponential Wave Maps
9.Exponential Yang
Mills Connections
Index.
ISBN:9783034805346
Series:e-books
Series:SpringerLink (Online service)
Series:Frontiers in Mathematics, 1660-8046
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis , Differential equations, partial , Global differential geometry , Mathematical optimization
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Call number:SPRINGER-2013-9781461486992:ONLINE Show nearby items on shelf
Title:Geodesic Convexity in Graphs [electronic resource]
Author(s): Ignacio M Pelayo
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
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Note:Geodesic Convexity in Graphsis devoted to the study of the geodesic convexity on finite, simple, connected graphs. The first chapter includes the main definitions and results on graph theory, metric graph theory and graph pathconvexities. The followi ng chapters focus exclusively on the geodesic convexity, including motivation and background, specific definitions, discussion and examples, results, proofs, exercises and open problems. The main and most studied parameters involving geodesic convexity in graphs are both the geodetic and the hull number which are defined as the cardinality of minimum geodetic and hull set, respectively. This text reviews various results, obtained duringthe last one and a half decade, relating these two invariants and some others such as convexity number, Steiner number, geodetic iteration number, Helly number, and Caratheodory number to a wide range a contexts, including products,boundary-type vertex sets, and perfect graph families. This monograph can serve as a suppleme nt to a half-semester graduatecourse in geodesic convexitybut is primarilya guide for postgraduates and researchers interested in topicsrelated to metric graph theory and graph convexity theory.
Note:Springer eBooks
ISBN:9781461486992
Series:e-books
Series:SpringerLink (Online service)
Series:SpringerBriefs in Mathematics, 2191-8198
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differential equations, partial , Global differential geometry
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Call number:SPRINGER-2013-9781461485261:ONLINE Show nearby items on shelf
Title:Hermitian Analysis [electronic resource] : From Fourier Series to Cauchy-Riemann Geometry
Author(s): John P D'Angelo
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Hermitian Analysis: From Fourier Series to Cauchy-Riemann Geometry provides a coherent, integrated look at various topics from analysis. It begins with Fourier series, continues with Hilbert spaces, discusses the Fourier transformon the real line, an d then turns to the heart of the book: geometric considerations in several complex variables. The final chapter includes complex differential forms, geometric inequalities from one and several complex variables,finite unitary groups, proper mappings, and naturally leads to the Cauchy-Riemann geometry of the unit sphere. The book thus takes the reader from the unit circle to the unit sphere. This textbook will be a useful resource forupper-undergraduate students who intend to continue with mathematics, gra duate students interested in analysis, and researchers interested in some basic aspects of CR Geometry. It will also be useful for students in physics andengineering, as it includes topics in harmonic analysis arising in these subjects.The inclusion of an appendix and more than 270 exercises makes this book suitable for a capstone undergraduate Honors class
Note:Springer eBooks
Contents:Preface
Introduction to Fourier series
Hilbert spaces
Fourier transform on R
Geometric considerations
Appendix
References
Index.
ISBN:9781461485261
Series:e-books
Series:SpringerLink (Online service)
Series:Cornerstones, 2197-182X
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Fourier analysis , Differential Equations , Global differential geometry
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Call number:SPRINGER-2013-9781461479246:ONLINE Show nearby items on shelf
Title:Geometric Analysis of the Bergman Kernel and Metric [electronic resource]
Author(s): Steven G Krantz
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This text provides a masterful and systematic treatment of all the basic analytic and geometric aspects of Bergman's classic theory of the kernel and its invariance properties. These include calculation, invariance properties,boundary asymptotics, an d asymptotic expansion of the Bergman kernel and metric.Moreover, itpresents a unique compendium of results with applications to function theory, geometry, partial differential equations, and interpretationsin the language of functional analysis, with emp hasis on the several complex variables context. Several of these topics appear here for the first time in book form. Each chapter includes illustrative examples and a collection ofexercises which will be of interest to both graduate students and experienc ed mathematicians. Graduate students who have taken courses in complex variables and have a basic background in real and functional analysis will find thistextbook appealing. Applicable courses for either main or supplementary usage include those in compl ex variables, several complex variables, complex differential geometry, and partial differential equations. Researchers in complexanalysis, harmonic analysis, PDEs, and complex differential geometry will also benefit from the thorough treatment of the man y exciting aspects of Bergman's theory
Note:Springer eBooks
Contents:Preface
1. Introductory Ideas
2.The Bergman Metric
3. Geometric and Analytic Ideas
4. Partial Differential Equations
5. Further Geometric Explorations
6. Additional Analytic Topics
7. Curvature of the Bergman Metric
8. Concluding Remarks
Table of Notation
Bibliography
Index
ISBN:9781461479246
Series:e-books
Series:SpringerLink (Online service)
Series:Graduate Texts in Mathematics, 0072-5285 : v268
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Functional analysis , Differential equations, partial , Global differential geometry
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Call number:SPRINGER-2013-9781461478676:ONLINE Show nearby items on shelf
Title:Introduction to Tensor Analysis and the Calculus of Moving Surfaces [electronic resource]
Author(s): Pavel Grinfeld
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This text is meant to deepen its readers understanding of vector calculus, differential geometry and related subjects in applied mathematics. Designed for advanced undergraduate and graduate students, this text invites itsaudience to take a fresh loo k at previously learned material through the prism of tensor calculus. Once the framework is mastered, the student is introduced to new material which includes differential geometry on manifolds, shapeoptimization, boundary perturbation, and dynamic fluid film equations. Tensor calculus is a powerful tool that combines the geometric and analytical perspectives and enables us to take full advantage of the computational utility ofcoordinate systems. The tensor approach can be of benefit to members of all te chnical sciences including mathematics and all engineering disciplines. If calculus and linear algebra are central to the readers scientific endeavors,tensor calculus is indispensable. The language of tensors, originally championed by Einstein, is as fund amental as the languages of calculus and linear algebra and is one that every technical scientist ought to speak. The tensortechnique, invented at the turn of the 20th century, is now considered classical. Yet, as the author shows, it remains remarkably v ital and relevant. The authors skilled lecturing capabilities are evident by the inclusion ofinsightful examples and a plethora of exercises. A great deal of material is devoted to the geometric fundamentals, the mechanics of change of variables, the prop er use of the tensor notation, and the discussion of the interplaybetween algebra and geometry. The early chapters have many words and few equations. The definition of a tensor comes only in Chapter 6 when the reader is ready for it. While this text main tains a reasonable level of rigor, it takesgreat care to avoid formalizing the subject. The last part of the textbook is devoted to the calculus of moving surfaces. It is the first textboo
Note:Springer eBooks
Contents:Preface
Why Tensor Calculus?
1. Rules of the Game
2. Coordinate Systems and the Role of Tensor Calculus
3. Change of Coordinates
4. Tensor Description of Euclidean Spaces
5. The Tensor Property
6. Covariant Differentiation
7. Determinants and the Levi
Civita Symbol
8. Tensor Description of Surfaces
9. Covariant Derivative of Tensors with Surface Indices
10. The Curvature Tensor
11. Covariant Derivative of Tensors with Spatial Indices
12. Integration and Gauss's Theorem
13. Intrinsic Features of Embedded Surfaces
14. Further Topics in Differential Ge
ISBN:9781461478676
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Matrix theory , Global differential geometry , Mathematical optimization
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Call number:SPRINGER-2013-9781461477327:ONLINE Show nearby items on shelf
Title:First Steps in Differential Geometry [electronic resource] : Riemannian, Contact, Symplectic
Author(s): Andrew McInerney
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Differential geometry arguably offers the smoothest transition from the standard university mathematics sequence of the first four semesters in calculus, linear algebra, and differential equations to the higher levels ofabstraction and proof encounte red at the upper division by mathematics majors. Today it is possible to describe differential geometry as the study of structures on the tangent space, and this text develops this point of view. Thisbook, unlike other introductory texts in differential g eometry, develops the architecture necessary to introduce symplectic and contact geometry alongside its Riemannian cousin. The main goal of this book is to bring the undergraduatestudent who already has a solid foundation in the standard mathematics curri culum into contact with the beauty of higher mathematics. In particular, the presentation here emphasizes the consequences of a definition and the careful useof examples and constructions in order to explore those consequences
Note:Springer eBooks
Contents:Basic Objects and Notation
Linear Algebra Essentials
Advanced Calculus
Differential Forms and Tensors
Riemannian Geometry
Contact Geometry
Symplectic Geometry
References
Index
ISBN:9781461477327
Series:e-books
Series:SpringerLink (Online service)
Series:Undergraduate Texts in Mathematics, 0172-6056
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis , Global differential geometry , Cell aggregation Mathematics
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Call number:SPRINGER-2013-9781461464037:ONLINE Show nearby items on shelf
Title:Arithmetic and Geometry of K3 Surfaces and CalabiYau Threefolds [electronic resource]
Author(s): Radu Laza
Matthias Schtt
Noriko Yui
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:In recent years, research in K3 surfaces and CalabiYau varieties has seen spectacular progress from both the arithmetic and geometric points of view, which in turn continues to have a huge influence and impact in theoreticalphysicsin particular, in s tring theory. The workshop on Arithmetic and Geometry of K3 surfaces and CalabiYau threefolds, held at the Fields Institute (August 1625, 2011), aimed to give a state-of-the-art survey of thesenew developments. This proceedings volume includes a represent ative sampling of the broad range of topics covered by the workshop. While the subjects range from arithmetic geometry through algebraic geometry and differential geometryto mathematical physics, the papers are naturally related by the common theme of Cal abiYau varieties. With thelarge variety of branches of mathematics and mathematical physics touched upon, this area reveals many deep connectionsbetween subjects previously considered unrelated. Unlike most other conferences, the 2011 CalabiYau workshop s tarted withthree days of introductory lectures. A selection offour of these lectures is included in this volume. Theselectures can be used as a starting point for graduate students and other junior researchers, or as a guide to the subject
Note:Springer eBooks
Contents:
Preface
Introduction
List of Participants
K3 and Enriques Surfaces (S. Kondo)
Transcendental Methods in the Study of Algebraic Cycles with a Special Emphasis on CalabiYau Varieties (J.D. Lewis)
Two Lectures on the Arithmetic of K3 Surfaces (M. Schtt)
Modularity of CalabiYau Varieties (N. Yui)
Explicit Algebraic Coverings of a Pointed Torus (A. Anema, J. Top)
Elliptic Fibrations on the Modular Surface Associated to 1(8)
Universal Kummer Families over Shimura Curves (A. Besser, R. Livn)
Numerical Trivial Automorphisms of Enriques Surfaces in Arbitrary Ch
ISBN:9781461464037
Series:e-books
Series:SpringerLink (Online service)
Series:Fields Institute Communications, 1069-5265 : v67
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Global differential geometry , Number theory
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Call number:SPRINGER-2013-9781461459811:ONLINE Show nearby items on shelf
Title:The Implicit Function Theorem [electronic resource] History, Theory, and Applications
Author(s): Steven G Krantz
Harold R Parks
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The implicit function theorem is part ofthe bedrock of mathematical analysis and geometry. Finding its genesis in eighteenth century studies of real analytic functions and mechanics, the implicit and inverse function theoremshave now blossomed into p owerful tools in the theories of partial differential equations, differential geometry, and geometric analysis. There are many different forms of the implicit function theorem, including (i) the classicalformulation forCkfunctions, (ii) formulations in ot her function spaces, (iii) formulations for non-smooth functions, and (iv) formulations for functions with degenerate Jacobian. Particularly powerful implicit function theorems,such as the NashMoser theorem, have been developed for specific applications ( e.g., the imbedding of Riemannian manifolds). All of these topics, and many more, are treated in the present uncorrected reprint of thisclassicmonograph. Originally published in 2002,The Implicit Function Theoremis an accessible and thorough treatment of implicit and inverse function theorems and their applications. It will be of interest to mathematicians,graduate/advanced undergraduate students, and to those who apply mathematics. The book unifies disparate ideas that have played an important role in mo dern mathematics. It serves to document and placein context a substantial body ofmathematical ideas
Note:Springer eBooks
Contents:Preface
Introduction to the Implicit Function Theorem
History
Basic Ideas
Applications
Variations and Generalizations
Advanced Implicit Function Theorems
Glossary
Bibliography
Index
ISBN:9781461459811
Series:e-books
Series:SpringerLink (Online service)
Series:Modern Birkhuser Classics
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Differential Equations , Differential equations, partial , Global differential geometry
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Call number:SPRINGER-2013-9781461448976:ONLINE Show nearby items on shelf
Title:Recent Trends in Lorentzian Geometry [electronic resource]
Author(s): Miguel Snchez
MIguel Ortega
Alfonso Romero
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:Traditionally, Lorentzian geometry has been used as a necessary tool to understand general relativity,as well as to explore new genuine geometric behaviors, far from classical Riemannian techniques. Recent progress has attracteda renewed interest in this theoryfor many researchers: long-standing global open problems have been solved, outstanding Lorentzian spaces and groups have been classified, new applications to mathematical relativity and high energyphysics have been found, and further connection s with other geometries have been developed. Samplesof these fresh trends are presented in this volume, based on contributions from the VI International Meeting on LorentzianGeometry, held at the University of Granada, Spain, in September, 2011. Topics s uch as geodesics, maximal,trapped and constant mean curvature submanifolds, classifications of manifolds with relevant symmetries, relations betweenLorentzian and Finslerian geometries, and applications to mathematical physics are included. This book wil l be suitable for a broad audience of differential geometers, mathematical physicists and relativists, and researchers inthe field
Note:Springer eBooks
ISBN:9781461448976
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Proceedings in Mathematics & Statistics, 2194-1009 : v26
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Discrete groups , Global differential geometry
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Call number:SPRINGER-2013-9781461421764:ONLINE Show nearby items on shelf
Title:Fractal Geometry, Complex Dimensions and Zeta Functions [electronic resource] : Geometry and Spectra of Fractal Strings
Author(s): Michel L Lapidus
Machiel van Frankenhuijsen
Date:2013
Edition:2nd ed. 2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings that is, one-dimensional drums with fractal boundary. This second edition of Fractal Geometry,Complex Dimensions and Ze ta Functions will appeal to students and researchers in number theory, fractal geometry, dynamical systems, spectral geometry, complex analysis, distribution theory, and mathematical physics. The significantstudies and problems illuminated in this work ma y be used in a classroom setting at the graduate level. Key Features include: The Riemann hypothesis is given a natural geometric reformulation in the context ofvibrating fractal strings Complex dimensions of a fractal string are studied in detail, and used to understand the oscillations intrinsic to the corresponding fractal geometries and frequency spectra Explicit formulas are extended to apply to the geometric, spectral, and dynamical zeta functions associated with a fractal Examples of such explic it formulas include a Prime Orbit Theorem witherror term for self-similar flows, and a geometric tube formula The method of Diophantine approximation is used to study self-similar strings and flows Analytical and geometric methods are used toobtain new results about the vertical distribution of zeros of number-theoretic and other zeta functions The unique viewpoint of this book culminates in the definition of fractality as the presence of nonreal complex dimensions. Thefinal chapter (13) is new to the s econd edition and discusses several new topics, results obtained since the publication of the first edition, and suggestions for future developments in the field. Review of the First Edition: Thebook is self contained, the material organized in chapters preceded by an introduction and finally there are some interesting applications of the theor
Note:Springer eBooks
Contents:Preface
Overview
Introduction
1. Complex Dimensions of Ordinary Fractal Strings
2. Complex Dimensions of Self
Similar Fractal Strings
3. Complex Dimensions of Nonlattice Self
Similar Strings
4. Generalized Fractal Strings Viewed as Measures
5. Explicit Formulas for Generalized Fractal Strings
6. The Geometry and the Spectrum of Fractal Strings
7. Periodic Orbits of Self
Similar Flows
8. Fractal Tube Formulas
9. Riemann Hypothesis and Inverse Spectral Problems
10. Generalized Cantor Strings and their Oscillations
11. Critical Zero of Zeta Functions
12 F
ISBN:9781461421764
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Monographs in Mathematics, 1439-7382
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differentiable dynamical systems , Functional analysis , Global analysis , Differential equations, partial , Number theory
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Call number:SPRINGER-2013-9780817683702:ONLINE Show nearby items on shelf
Title:Geography of Order and Chaos in Mechanics [electronic resource] : Investigations of Quasi-Integrable Systems with Analytical, Numerical, and Graphical Tools
Author(s): Bruno Cordani
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This original monograph aims to explore the dynamics in the particular but very important and significant case of quasi-integrable Hamiltonian systems, or integrable systems slightly perturbed by other forces. With both analyticand numerical methods, the book studies several of these systemsincluding for example the hydrogen atom or the solar system, with the associated Arnold webthrough modern tools such as the frequency-modified fourier transform,wavelets, and the frequency-modulation indicator. Me anwhile, it draws heavily on the more standard KAM and Nekhoroshev theorems. Geography of Order and Chaos in Mechanics contains many figures that illuminate its concepts in novelways, but perhaps its most useful feature is its inclusion of software to rep roduce the various numerical experiments. The graphical user interfaces of five supplied MATLAB programs allows readers without any knowledge of computerprogramming to visualize and experiment with the distribution of order, chaos and resonances in variou s Hamiltonian systems. This monograph will be a valuable resource for professional researchers and certain advanced undergraduatestudents in mathematics and physics, but mostly will be an exceptional reference for Ph.D. students with an interest in pertur bation theory
Note:Springer eBooks
Contents:Preface
List of Figures
1 Introductory Survey
2 Analytical Mechanics and Integrable Systems
3 Perturbation Theory
4 Numerical Tools I: ODE Integration
5 Numerical Tools II: Detecting Order, Chaos, and Resonances
6 The Kepler Problem
7 TheKEPLER Program
8 Some Perturbed Keplerian Systems
9 The Multi
Body Gravitational Problem
Bibliography
Index
ISBN:9780817683702
Series:e-books
Series:SpringerLink (Online service)
Series:Progress in Mathematical Physics : v64
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differential equations, partial , Global differential geometry , Mathematical physics
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Call number:SPRINGER-2012-9788847019416:ONLINE Show nearby items on shelf
Title:Curves and Surfaces [electronic resource]
Author(s): Marco Abate
Francesca Tovena
Date:2012
Publisher:Milano : Springer Milan : Imprint: Springer
Size:1 online resource
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Note:The book provides an introduction to Differential Geometry of Curves and Surfaces. The theory of curves starts with a discussion of possible definitions of the concept of curve, proving in particular the classification of1-dimensional manifolds. We t hen present the classical local theory of parametrized plane and space curves (curves in n-dimensional space are discussed in the complementary material): curvature, torsion, Frenets formulas and thefundamental theorem of the local theory of curves. Then, after a self-contained presentation of degree theory for continuous self-maps of the circumference, we study the global theory of plane curves, introducing winding and rotationnumbers, and proving the Jordan curve theorem for curves of class C2, and Hopf theorem on the rotation number of closed simple curves. The local theory of surfaces begins with a comparison of the concept of parametrized (i.e.,immersed) surface with the concept of regular (i.e., embedded) surface. We then develop the basic different ial geometry of surfaces in R3: definitions, examples, differentiable maps and functions, tangent vectors (presented both asvectors tangent to curves in the surface and as derivations on germs of differentiable functions we shall consistently use both app roaches in the whole book) and orientation. Next we study the several notions of curvature on asurface, stressing both the geometrical meaning of the objects introduced and the algebraic/analytical methods needed to study them via the Gauss map, up to the proof of Gauss Teorema Egregium. Then we introduce vector fields on asurface (flow, first integrals, integral curves) and geodesics (definition, basic properties, geodesic curvature, and, in the complementary material, a full proof of minimizing properti es of geodesics and of the Hopf-Rinow theorem forsurfaces). Then we shall present a proof of the celebrated Gauss-Bonnet theorem, both in its local and in its global form, using basic properties
Note:Springer eBooks
ISBN:9788847019416
Series:e-books
Series:SpringerLink (Online service)
Series:UNITEXT, 2038-5714
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer vision , Computer science , Geometry , Global differential geometry
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Call number:SPRINGER-2012-9783642298462:ONLINE Show nearby items on shelf
Title:Coulomb Frames in the Normal Bundle of Surfaces in Euclidean Spaces [electronic resource] : Topics from Differential Geometry and Geometric Analysis of Surfaces
Author(s): Steffen Frhlich
Date:2012
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book is intended for advanced students and young researchers interested in the analysis of partial differential equations and differential geometry. It discusses elementary concepts of surface geometry in higher-dimensionalEuclidean spaces, in p articular the differential equations of Gauss-Weingarten together with various integrability conditions and corresponding surface curvatures. It includes a chapter on curvature estimates for such surfaces, and,using results from potential theory and harmo nic analysis, it addresses geometric and analytic methods to establish the existence and regularity of Coulomb frames in their normal bundles, which arise as critical points for a functionalof total torsion
Note:Springer eBooks
Contents:Surface Geometry
Elliptic Systems
Normal Coulomb Frames in R4
Normal Coulomb Frames in Rn+2
ISBN:9783642298462
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v2053
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functions of complex variables , Differential equations, partial , Global differential geometry
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Call number:SPRINGER-2012-9783642256202:ONLINE Show nearby items on shelf
Title:A Theory of Branched Minimal Surfaces [electronic resource]
Author(s): Anthony Tromba
Date:2012
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
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Note:One of the most elementary questions in mathematics is whether an area minimizing surface spanning a contour in three space is immersed or not i.e. does its derivative have maximal rank everywhere. The purpose of this monographis to present an elemen tary proof of this very fundamental and beautiful mathematical result. The exposition follows the original line of attack initiated by Jesse Douglas in his Fields medal work in 1931, namely use Dirichlet's energyas opposed to area. Remarkably, the author shows how to calculate arbitrarily high orders of derivatives of Dirichlet's energy defined on the infinite dimensional manifold of all surfaces spanning a contour, breaking new ground in theCalculus of Variations, where normally only the second derivativ e or variation is calculated. The monograph begins with easy examples leading to a proof in a large number of cases that can be presented in a graduate course in eithermanifolds or complex analysis. Thus this monograph requires only the most basic knowled ge of analysis, complex analysis and topology and can therefore be read by almost anyone with a basic graduate education
Note:Springer eBooks
Contents:1.Introduction
2.Higher order Derivatives of Dirichlets' Energy
3.Very Special Case The Theorem for n + 1 Even and m + 1 Odd
4.The First Main Theorem Non
Exceptional Branch Points
5.The Second Main Theorem: Exceptional Branch Points The Condition k > l
6.Exceptional Branch Points Without The Condition k > l
7.New Brief Proofs of the Gulliver
Osserman
Royden Theorem
8.Boundary Branch Points
Scholia
Appendix
Bibliography
ISBN:9783642256202
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Monographs in Mathematics, 1439-7382
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functions of complex variables , Global analysis , Sequences (Mathematics) , Global differential geometry
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Call number:SPRINGER-2012-9783642255885:ONLINE Show nearby items on shelf
Title:Manfredo P. do Carmo Selected Papers [electronic resource]
Author(s): Manfredo P do Carmo
Keti Tenenblat
Date:2012
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
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Note:This volume of selected academic papers demonstrates the significance of the contribution to mathematics made by Manfredo P. do Carmo. Twice a Guggenheim Fellow and the winner of many prestigious national and international awards,the professor at the institute of Pure and Applied Mathematics in Rio de Janeiro is well known as the author of influential textbooks such as Differential Geometry of Curves and Surfaces. The area of differential geometry is the mainfocus of this selection, though it also co ntains do Carmo's own commentaries on his life as a scientist as well as assessment of the impact of his researches and a complete list of his publications. Aspects covered in the featuredpapers include relations between curvature and topology, convexity and rigidity, minimal surfaces, and conformal immersions, among others. Offering more than just a retrospective focus, the volume deals with subjects of currentinterest to researchers, including a paper co-authored with Frank Warner on the convexity of hy persurfaces in space forms. It also presents the basic stability results for minimal surfaces in the Euclidean space obtained by the authorand his collaborators. Edited by do Carmo's first student, now a celebrated academic in her own right, this collecti on pays tribute to one of the most distinguished mathematicians
Note:Springer eBooks
Contents:Preface
A Summary of the Scientific Activities of Manfredo P. do Carmo
Summary of thePapers in this Volume by Manfredo P. do Carmo
Contributions
Complete List of Publications of Manfredo P. do Carmo
List of D.Sc. Students of Manfredo P. do Carmo
ISBN:9783642255885
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry , Global differential geometry , Cell aggregation Mathematics
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Call number:SPRINGER-2012-9783642248887:ONLINE Show nearby items on shelf
Title:Finsler Geometry [electronic resource] : An Approach via Randers Spaces
Author(s): Xinyue Cheng
Zhongmin Shen
Date:2012
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
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Note:Finsler Geometry: An Approach via Randers Spaces exclusively deals with a special class of Finsler metrics -- Randers metrics, which are defined as the sum of a Riemannian metric and a 1-form. Randers metrics derive from theresearch on General Relati vity Theory and have been applied in many areas of the natural sciences. They can also be naturally deduced as the solution of the Zermelo navigation problem. The book provides readers not only with essentialfindings on Randers metrics but also the core i deas and methods which are useful in Finsler geometry. It will be of significant interest to researchers and practitioners working in Finsler geometry, even in differential geometry orrelated natural fields. Xinyue Cheng is a Professor at the School of Ma thematics and Statistics of Chongqing University of Technology, China. Zhongmin Shen is a Professor at the Department of Mathematical Sciences of Indiana UniversityPurdue University, USA
Note:Springer eBooks
Contents:Randers Spaces
Randers Metrics and Geodesics
Randers Metrics of Isotropic S
Curvature
Riemann Curvature and Ricci Curvature
Projective Geometry of Randers Spaces
Randers Metrics with Special Riemann Curvature Properties
Randers Metrics of Weakly Isotropic Flag Curvature
Projectively Flat Randers Metrics
Conformal Geometry of Randers Metrics
Dually Flat Randers Metrics
ISBN:9783642248887
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry , Global differential geometry , Mathematical physics
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