An invitation to optimal transport, Wasserstein distances, and gradient flows
Alessio Figalli (Author), Federico Glaudo (Author)
"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. The book is suitable for a course at the graduate level and also includes an appendix with a series of exercises along with their solutions. The present 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."-- publisher
eBook, English, 2023
Second edition
EMS Press, Berlin, Germany, 2023