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Partial regularity of optimal transport maps

Introductory Workshop on Optimal Transport: Geometry and Dynamics August 26, 2013 - August 30, 2013

August 29, 2013 (11:00 AM PDT - 12:00 PM PDT)
Speaker(s): Guido De Philippis (Hausdorff Research Institute for Mathematics, University of Bonn)
Location: MSRI: Simons Auditorium

Abstract We prove that for general smooth cost functions on the Euclidean space, or for the cost given by the squared distance on a Riemannian manifold, optimal transport maps between smooth densities are smooth outside a closed set of measure zero.(joint work with Alessio Figalli)
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