Graduate Studies in Mathematics
Volume: 58; 2003; 370 pp; Hardcover
MSC: Primary 49; Secondary 35; 60

Print ISBN: 978-0-8218-3312-4
Product Code: GSM/58
List Price: $74.00
AMS Member Price: $59.20
MAA Member Price: $66.60

Electronic ISBN: 978-1-4704-1804-5
Product Code: GSM/58.E
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Topics in Optimal Transportation

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Cédric Villani

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.

Readership

Graduate students and research mathematicians interested in probability theory, functional analysis, isoperimetry, partial differential equations, and meteorology.

Reviews & Endorsements

Villani writes with enthusiasm, and his approachable style is aided by pleasant typography. The exposition is far from rigid. ... As an introduction to an active and rapidly growing area of research, this book is greatly to be welcomed. Much of it is accessible to the novice research student possessing a solid background in real analysis, yet even experienced researchers will find it a stimulating source of novel applications, and a guide to the latest literature.

-- Geoffrey Burton, Bulletin of the LMS

Cedric Villani's book is a lucid and very readable documentation of the tremendous recent analytic progress in ‘optimal mass transportation’ theory and of its diverse and unexpected applications in optimization, nonlinear PDE, geometry, and mathematical physics.

-- Lawrence C. Evans, University of California at Berkeley

The book is clearly written and well organized and can be warmly recommended as an introductory text to this multidisciplinary area of research, both pure and applied - the mass transportation problem.

-- Studia Universitatis Babes-BolyaiMathematica

This is a very interesting book: it 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.

-- Olaf Ninnemann for Zentralblatt MATH

Topics in Optimal Transportation

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Print Product Code: GSM/58

Online Product Code: GSM/58.E

Title (HTML): Topics in Optimal Transportation

Author(s) (Product display): Cédric Villani

Affiliation(s) (HTML): École Normale Supérieure de Lyon, Lyon, France

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Book Series Name: Graduate Studies in Mathematics

Volume: 58

Publication Month and Year: 2003-03-25

Page Count: 370

Cover Type: Hardcover

Print ISBN-13: 978-0-8218-3312-4

Online ISBN 13: 978-1-4704-1804-5

Print ISSN: 1065-7339

Online ISSN: 1065-7339

Primary MSC: 49

Secondary MSC: 35; 60

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Readership:

Graduate students and research mathematicians interested in probability theory, functional analysis, isoperimetry, partial differential equations, and meteorology.

Reviews:

-- Geoffrey Burton, Bulletin of the LMS

-- Lawrence C. Evans, University of California at Berkeley

-- Studia Universitatis Babes-BolyaiMathematica

-- Olaf Ninnemann for Zentralblatt MATH

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Cover
- Cover
Title page
- Title page
Contents
- Contents
Preface
- Preface
Notation
- Notation
Introduction
- Introduction
The Kantorovich duality
- The Kantorovich duality
Index
- Index

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Topics in Optimal Transportation

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Table of Contents

Topics in Optimal Transportation

Free Attachments

Cover

Title page

Contents

Preface

Notation

Introduction

The Kantorovich duality

Index