Invitation to optimal transport, Wasserstein distances, and gradient flows
- 2nd ed.
- Berlin : European Mathematical Society, 2021
- 146 p. ; 24 cm
- EMS textbooks in mathematics .
Includes bibliographical references.
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.
9783985470501
Wasserstein distance Displacement convexity Gradient flows Kantorovich duality Optimal transport maps Otto's calculus Minkowski inequality JKO scheme Measure theory