ANALYSIS SEMINAR

12/1/2008

Alessio Figalli
Université de Nice Sophia-Antipolis and Ecole Polytechnique

Regularity results for optimal transport maps on Riemannian manifolds

In this talk I will describe some recent developments of the regularity theory for optimal transport maps on Riemannian manifolds, when the cost function is given by the squared distance. We will see in particular that the regularity theory of optimal maps allows to study the geometry of the cut locus of the manifold.