Optimal Transport

Cédric Villani, geboren 1973, gehört zu den weltweit führenden und innovativsten Mathematikern. Für seine Forschung erhielt er mehrere Preise, u.a. 2010 die renommierte Fields-Medaille. 2009 erhielt er den Henri-Poincaré-Preis, den Fermat-Preis und 2008 den EMS-Preis. Villani ist Professor für Mathematik an der École Normale Supérieure in Lyon und Direktor des Institut Henri Poincaré in Paris..

Introduction.- Qualitative Description of Optimal Transport.- Optimal Transport and Riemannian Geometry.- Synthetic Treatment of Ricci Curvature.- Conclusions and Open Problems.

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)

"The book is an in-depth, modern, clear exposition of the advanced theory of optimal transport, and it tries to put together in a unified way almost all the recent developments of the theory. ... the book is extremely well written and very pleasant to read. ... I strongly recommend this excellent book to every researcher or graduate student in the field of optimal transport. ... of interest to many mathematicians in different areas, who are simply interested in having an overview of the subject." (Alessio Figalli, Bulletin of the American Mathematical Society, Vol. 47 (4), February, 2010)

»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)

»The book is an in-depth, modern, clear exposition of the advanced theory of optimal transport, and it tries to put together in a unified way almost all the recent developments of the theory. the book is extremely well written and very pleasant to read. I strongly recommend this excellent book to every researcher or graduate student in the field of optimal transport. of interest to many mathematicians in different areas, who are simply interested in having an overview of the subject.« (Alessio Figalli, Bulletin of the American Mathematical Society, Vol. 47 (4), February, 2010)

»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)