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

  • Alessio Figalli

    ETH Zürich, Switzerland
  • Federico Glaudo

    ETH Zürich, Switzerland
An Invitation to Optimal Transport, Wasserstein Distances, and Gradient Flows cover
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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.