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| Author | : Newton Tenney Peck |
| Publisher | : |
| Total Pages | : 96 |
| Release | : 1966 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : |
| Publisher | : |
| Total Pages | : 744 |
| Release | : 1973 |
| Genre | : Union catalogs |
| ISBN | : |
Includes entries for maps and atlases.
| Author | : |
| Publisher | : |
| Total Pages | : 744 |
| Release | : 1973 |
| Genre | : Union catalogs |
| ISBN | : |
| Author | : Jaroslav Lukeš |
| Publisher | : Walter de Gruyter |
| Total Pages | : 732 |
| Release | : 2010 |
| Genre | : Mathematics |
| ISBN | : 3110203200 |
This monograph presents the state of the art of convexity, with an emphasis to integral representation. The exposition is focused on Choquet's theory of function spaces with a link to compact convex sets. An important feature of the book is an interplay between various mathematical subjects, such as functional analysis, measure theory, descriptive set theory, Banach spaces theory and potential theory. A substantial part of the material is of fairly recent origin and many results appear in the book form for the first time. The text is self-contained and covers a wide range of applications. From the contents: Geometry of convex sets Choquet theory of function spaces Affine functions on compact convex sets Perfect classes of functions and representation of affine functions Simplicial function spaces Choquet's theory of function cones Topologies on boundaries Several results on function spaces and compact convex sets Continuous and measurable selectors Construction of function spaces Function spaces in potential theory and Dirichlet problem Applications
| Author | : |
| Publisher | : |
| Total Pages | : 744 |
| Release | : 1964 |
| Genre | : American literature |
| ISBN | : |
| Author | : Cédric Villani |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 970 |
| Release | : 2008-10-26 |
| Genre | : Mathematics |
| ISBN | : 3540710507 |
At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and John Mather launched a revolution in the venerable field of optimal transport founded by G. Monge in the 18th century, which has made breathtaking forays into various other domains of mathematics ever since. The author presents a broad overview of this area, supplying complete and self-contained proofs of all the fundamental results of the theory of optimal transport at the appropriate level of generality. Thus, the book encompasses the broad spectrum ranging from basic theory to the most recent research results. PhD students or researchers can read the entire book without any prior knowledge of the field. A comprehensive bibliography with notes that extensively discuss the existing literature underlines the book’s value as a most welcome reference text on this subject.
| Author | : Danny Calegari |
| Publisher | : Mathematical Society Of Japan Memoirs |
| Total Pages | : 209 |
| Release | : 2009-06 |
| Genre | : Mathematics |
| ISBN | : 9784931469532 |
This book is a comprehensive introduction to the theory of stable commutator length, an important subfield of quantitative topology, with substantial connections to 2-manifolds, dynamics, geometric group theory, bounded cohomology, symplectic topology, and many other subjects. We use constructive methods whenever possible, and focus on fundamental and explicit examples. We give a self-contained presentation of several foundational results in the theory, including Bavard's Duality Theorem, the Spectral Gap Theorem, the Rationality Theorem, and the Central Limit Theorem. The contents should be accessible to any mathematician interested in these subjects, and are presented with a minimal number of prerequisites, but with a view to applications in many areas of mathematics.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets
| Author | : Filippo Santambrogio |
| Publisher | : Birkhäuser |
| Total Pages | : 376 |
| Release | : 2015-10-17 |
| Genre | : Mathematics |
| ISBN | : 3319208284 |
This monograph presents a rigorous mathematical introduction to optimal transport as a variational problem, its use in modeling various phenomena, and its connections with partial differential equations. Its main goal is to provide the reader with the techniques necessary to understand the current research in optimal transport and the tools which are most useful for its applications. Full proofs are used to illustrate mathematical concepts and each chapter includes a section that discusses applications of optimal transport to various areas, such as economics, finance, potential games, image processing and fluid dynamics. Several topics are covered that have never been previously in books on this subject, such as the Knothe transport, the properties of functionals on measures, the Dacorogna-Moser flow, the formulation through minimal flows with prescribed divergence formulation, the case of the supremal cost, and the most classical numerical methods. Graduate students and researchers in both pure and applied mathematics interested in the problems and applications of optimal transport will find this to be an invaluable resource.
| Author | : Grigoriy Blekherman |
| Publisher | : SIAM |
| Total Pages | : 487 |
| Release | : 2013-03-21 |
| Genre | : Mathematics |
| ISBN | : 1611972280 |
An accessible introduction to convex algebraic geometry and semidefinite optimization. For graduate students and researchers in mathematics and computer science.
| Author | : Michael Davis |
| Publisher | : Princeton University Press |
| Total Pages | : 601 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 0691131384 |
The Geometry and Topology of Coxeter Groups is a comprehensive and authoritative treatment of Coxeter groups from the viewpoint of geometric group theory. Groups generated by reflections are ubiquitous in mathematics, and there are classical examples of reflection groups in spherical, Euclidean, and hyperbolic geometry. Any Coxeter group can be realized as a group generated by reflection on a certain contractible cell complex, and this complex is the principal subject of this book. The book explains a theorem of Moussong that demonstrates that a polyhedral metric on this cell complex is nonpositively curved, meaning that Coxeter groups are "CAT(0) groups." The book describes the reflection group trick, one of the most potent sources of examples of aspherical manifolds. And the book discusses many important topics in geometric group theory and topology, including Hopf's theory of ends; contractible manifolds and homology spheres; the Poincaré Conjecture; and Gromov's theory of CAT(0) spaces and groups. Finally, the book examines connections between Coxeter groups and some of topology's most famous open problems concerning aspherical manifolds, such as the Euler Characteristic Conjecture and the Borel and Singer conjectures.
