In this book we describe recent developments in the theory of optimal transportation, and some of its applications to fluid dynamics. Moreover we explore new va

This monograph presents a rigorous mathematical introduction to optimal transport as a variational problem, its use in modeling various phenomena, and its conne

The goal of Optimal Transport (OT) is to define geometric tools that are useful to compare probability distributions. Their use dates back to 1781. Recent years

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 meas

This textbook is addressed to PhD or senior undergraduate students in mathematics, with interests in analysis, calculus of variations, probability and optimal t