An Invitation to Optimal Transport, Wasserstein Distances, and Gradient Flows

by Alessio Figalli, Federico Glaudo

This book provides a self-contained introduction to optimal transport, and it is intended as a starting point for any researcher who wants to enter into this beautiful subject. The presentation focuses on the essential topics of the Kantorovich duality, existence and uniqueness of optimal transport maps, Wasserstein distances, the JKO scheme, Otto's calculus, and Wasserstein gradient flows. At the end, a presentation of some selected applications of optimal transport is given. Suitable for a course at the graduate level, the book also includes an appendix with a series of exercises along with their solutions. The second edition contains a number of additions, such as a new section on the Brunn–Minkowski inequality, new exercises, and various corrections throughout the text.

146 pages, Hardcover

Published May 15, 2023