Introduction

Abstract

This book is devoted to a theory of gradient flows in spaces which are not necessarily endowed with a natural linear or differentiable structure. It is made of two parts, the first one concerning gradient flows in metric spaces and the second one devoted to gradient flows in the L²-Wasserstein space of probability measures on a separable Hilbert space X endowed with the Wasserstein L² metric (we consider the L^p-Wasserstein distance, p ∈ (1, ∞), as well).