This article gives a survey of recent research related to the Monge-Kantorovich problem.
Principle results are presented on the existence of solutions and their properties both in the …

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 …

The book is devoted to the theory of gradient flows in the general framework of metric
spaces, and in the more specific setting of the space of probability measures, which provide …

Includes material for a standard graduate class, advanced material not covered by the
standard course but necessary in order to read research literature in the area, and extensive …

This book provides the reader with the principal concepts and results related to differential
properties of measures on infinite dimensional spaces. In the finite dimensional case such …

В статье дается обзор недавних исследований, связанных с задачей Монжа-
Канторовича. Приведены основные результаты о существовании решений и их …

A new identity for the entropy of a non-linear image of a measure on is obtained, which
yields the well-known Talagrand's inequality. Triangular mappings on and are studied, that …

We develop the optimal transportation approach to modified log-Sobolev inequalities and to
isoperimetric inequalities. Various sufficient conditions for such inequalities are given. Some …

We study Sobolev a priori estimates for the optimal transportation T=∇Φ between
probability measures μ=e^-V\,dx and ν=e^-W\,dx on \bfR^d. Assuming uniform convexity of …

Let $\gamma $ be the standard Gaussian measure on $\mathbb {R}^ n $ and let $\mathcal
{P} _ {\gamma} $ be the space of probability measures that are absolutely continuous with …