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Publications mathématiques de l'IHÉS

, Volume 121, Issue 1, pp 81–112 | Cite as

Partial regularity for optimal transport maps

  • Guido De Philippis
  • Alessio Figalli
Article

Abstract

We prove that, for general cost functions on R n , or for the cost d 2/2 on a Riemannian manifold, optimal transport maps between smooth densities are always smooth outside a closed singular set of measure zero.

Keywords

Riemannian Manifold Partial Regularity Optimal Transport Optimal Transportation Smooth Density 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© IHES and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Scuola Normale SuperiorePisaItaly
  2. 2.Department of MathematicsThe University of Texas at AustinAustinUSA

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