Optimal Transport

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By: Cédric Villani

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Hardcover | 30 September 2008

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1000 Pages

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23.39 x 15.6 x 5.23

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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.

Industry Reviews

From the reviews: "The book is aimed to old and new problems of optimal transport. ! This meticulous work is based on very large bibliography ! that is converted into a very valuable monograph that presents many statements and theorems written specifically for this approach, complete and self-contained proofs of the most important results, and extensive bibliographical notes." (Mihail Voicu, Zentralblatt MATH, Vol. 1156, 2009) "This book wins the challenge to give a new and broad perspective on the multifacet topic of the optimal mass transport. ! Besides extensive and accurate references therein the reader will find comments on related questions barely touched upon in the main text as well as lively presentations on how ideas and results have developed. This book should prove useful both to the expert and to the beginner looking for a reference text on the subject." (Dario Cordero Erausquin, Mathematical Reviews, Issue 2010 f)

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You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Differential Calculus & Equations Geometry Differential & Riemannian Geometry Optimisation Linear Programming Calculus of Variations

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Published: 7th August 2014

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Published: 23rd August 2016

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Preface	p. VII
Conventions	p. XVII
Introduction	p. 1
Couplings and changes of variables	p. 5
Three examples of coupling techniques	p. 21
The founding fathers of optimal transport	p. 29
Qualitative description of optimal transport	p. 39
Basic properties	p. 43
Cyclical monotonicity and Kantorovich duality	p. 51
The Wasserstein distances	p. 93
Displacement interpolation	p. 113
The Monge-Mather shortening principle	p. 163
Solution of the Monge problem I: Global approach	p. 205
Solution of the Monge problem II: Local approach	p. 215
The Jacobian equation	p. 273
Smoothness	p. 281
Qualitative picture	p. 333
Optimal transport and Riemannian geometry	p. 353
Ricci curvature	p. 357
Otto calculus	p. 421
Displacement convexity I	p. 435
Displacement convexity II	p. 449
Volume control	p. 493
Density control and local regularity	p. 505
Infinitesimal displacement convexity	p. 525
Isoperimetric-type inequalities	p. 545
Concentration inequalities	p. 567
Gradient flows I	p. 629
Gradient flows II: Qualitative properties	p. 693
Gradient flows III: Functional inequalities	p. 719
Synthetic treatment of Ricci curvature	p. 731
Analytic and synthetic points of view	p. 735
Convergence of metric-measure spaces	p. 743
Stability of optimal transport	p. 773
Weak Ricci curvature bounds I: Definition and Stability	p. 795
Weak Ricci curvature bounds II: Geometric and analytic properties	p. 847
Conclusions and open problems	p. 903
References	p. 915
List of short statements	p. 957
List of figures	p. 965
Index	p. 967
Some notable cost functions	p. 971
Table of Contents provided by Ingram. All Rights Reserved.

Optimal Transport

Old and New

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Paperback

Paperback

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