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 theory: 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.

144 pages, Hardcover

Published August 1, 2021