A user's guide to optimal transport

Luigi Ambrosio (1) , Nicola Gigli (2)

1 SNS - SNS Pisa
2 LJAD - Laboratoire Jean Alexandre Dieudonné

This text is an expanded version of the lectures given by the first author in the 2009 CIME summer school of Cetraro. It provides a quick and reasonably account of the classical theory of optimal mass transportation and of its more recent developments, including the metric theory of gradient flows, geometric and functional inequalities related to optimal transportation, the first and second order differential calculus in the Wasserstein space and the synthetic theory of metric measure spaces with Ricci curvature bounded from below.

Domaines: Analyse classique [math.CA]

Luigi Ambrosio, Nicola Gigli. A user's guide to optimal transport. CIME summer school, 2009, Italy. ⟨hal-00769391⟩