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Topics in Optimal Transportation
 
Cédric Villani
Price : ₹ 1080.00
ISBN : 978-1-4704-2562-3
Language : English
Pages : 392
Binding : Paperback
Book Size : 180 x 240 mm
Year : 2016
Series : American Mathematical Society
Territorial Rights : Restricted
Imprint : No Image
 
 
About the Book

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.

Table of Contents

Introduction 
The Kantorovich duality 
Geometry of optimal transportation 
Brenier’s polar factorization theorem 
The Monge–Ampère 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

Contributors (Author(s), Editor(s), Translator(s), Illustrator(s) etc.)

Cédric Villani is Professor at the École Normale Supérieure de Lyon, Lyon, France

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