Topics in optimal transportation / Cédric Villani.
| Author/creator | Villani, Cédric, 1973- |
| Format | Book |
| Edition | Reprinted with corrections by the American Mathematical Society, 2016. |
| Publication | Providence, Rhode Island : American Mathematical Society, 2016. |
| Copyright Date | ©2003 |
| Description | xxii, 378 pages : illustrations ; 26 cm. |
| Supplemental Content | Access table of contents |
| Subjects |
| Series | Graduate studies in mathematics, 1065-7339 ; v. 58 Graduate studies in mathematics ; v. 58. ^A347883 |
| Contents | Ch. 1. The Kantorovich Duality -- Ch. 2. Geometry of Optimal Transportation -- Ch. 3. Brenier's Polar Factorization Theorem -- Ch. 4. The Monge-Ampere Equation -- Ch. 5. Displacement Interpolation and Displacement Convexity -- Ch. 6. Geometric and Gaussian Inequalities -- Ch. 7. The Metric Side of Optimal Transportation -- Ch. 8. A Differential Point of View on Optimal Transportation -- Ch. 9. Entropy Production and Transportation Inequalities -- Ch. 10. Problems -- Table of Short Statements. |
| Abstract | This is the first comprehensive introduction to the theory of mass transportation with its many - and sometimes unexpected - applications. In a novel approach to the subject, the book both surveys the topic and includes a chapter of problems, making it a particularly useful graduate textbook. In 1781, Gaspard Monge defined the problem of 'optimal transportation' (or the transferring of mass with the least possible amount of work), with applications to engineering in mind.In 1942, Leonid Kantorovich applied the newborn machinery of linear programming to Monge's problem, with applications to economics in mind. In 1987, Yann Brenier used optimal transportation to prove a new projection theorem on the set of measure preserving maps, with applications to fluid mechanics in mind. Each of these contributions marked the beginning of a whole mathematical theory, with many unexpected ramifications. Nowadays, the Monge-Kantorovich problem is used and studied by researchers from extremely diverse horizons, including probability theory, functional analysis, isoperimetry, partial differential equations, and even meteorology. Originating from a graduate course, the present volume is intended for graduate students and researchers, covering both theory and applications. Readers are only assumed to be familiar with the basics of measure theory and functional analysis. |
| Bibliography note | Includes bibliographical references (pages 353-367) and index. |
Availability
| Library | Location | Call Number | Status | Item Actions |
|---|---|---|---|---|
| Joyner | General Stacks | QA402.6 .V56 2016 | ✔ Available | Place Hold |