Publications mathématiques de l'IHÉS

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

Partial regularity for optimal transport maps

  • Guido De Philippis
  • Alessio FigalliEmail author


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.


Riemannian Manifold Partial Regularity Optimal Transport Optimal Transportation Smooth Density 
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© 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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