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

Beschreibung

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.

Autor*in

Alessio Figalli
ETH Zürich, Switzerland

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duality measure theory displacement convexity optimal transport Wasserstein distance gradient flows

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