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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
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

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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