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 …

In this introductory chapter we first give a brief historical review of optimal transport, then we
recall some basic definitions and facts from measure theory and Riemannian geometry, and …

Originally released in Italian, the series now publishes textbooks in English addressed to
students in mathematics worldwide. Some of the most successful books in the series have …

Why a new book on optimal transport? Were the two books by Fields Medalist Cédric Villani
not enough? And what about the Bible of Gradient Flows, the book by Luigi Ambrosio …

The marriage of analytic power to geometric intuition drives many of today's mathematical
advances, yet books that build the connection from an elementary level remain scarce. This …

Inspired by the numerical evidence of a potential 3D Euler singularity\cite
{luo2014potentially, luo2013potentially-2}, we prove finite time blowup of the 2D Boussinesq …

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 …

This book originates from a series of lectures given by the author at ETH Zürich during the
fall of 2014, in the framework of a Nachdiplomvorlesung, on the Monge–Ampère equation …

This text is an expanded version of the lectures given by the first author in the 2009 CIME
summer school of Cetraro. It provides a quick and reasonably account of the classical theory …

We obtain a sharp quantitative isoperimetric inequality for nonlocal s-perimeters, uniform
with respect to s bounded away from 0. This allows us to address local and global minimality …