Topics in Optimal Transportation

Cedric Villani, Ecole Normale Superieure de Lyon, France.

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

• IntroductionThe Kantorovich dualityGeometry of optimal transportationBrenier's polar factorization theoremThe Monge-Ampere equationDisplacement interpolation and displacement convexityGeometric and Gaussian inequalitiesThe metric side of optimal transportationA differential point of view on optimal transportationEntropy production and transportation inequalitiesProblemsBibliographyTable of short statementsIndex