Topics in optimal transportation
著者
書誌事項
Topics in optimal transportation
（Graduate studies in mathematics, v. 58）
American Mathematical Society, 2016
Reprinted with corrections
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注記
Bibliography: p. 353-367
Includes index
内容説明・目次
内容説明
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.
目次
Preface
Notation
Introduction
The Kantorovich duality
Geometry of optimal transportation
Brenier's polar factorization theorem
The Monge-Ampere equation
Displacement interpolation and displacement convexity
Geometric and Gaussian inequalities
The metric side of optimal transportation
A differential point of view on optimal transportation
Entropy production and transportation inequalities
Problems
Bibliography
Table of short statements
Index
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