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Partial regularity for optimal transport maps

Publications mathématiques de l'IHÉS volume 121, pages 81–112 (2015)Cite this 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.

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Author information

Authors and Affiliations

  1. Scuola Normale Superiore, p.za dei Cavalieri 7, 56126, Pisa, Italy

    Guido De Philippis

  2. Department of Mathematics, The University of Texas at Austin, 1 University Station C1200, Austin, TX, 78712, USA

    Alessio Figalli

Authors
  1. Guido De Philippis
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  2. Alessio Figalli
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Correspondence to Alessio Figalli.

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Cite this article

De Philippis, G., Figalli, A. Partial regularity for optimal transport maps. Publ.math.IHES 121, 81–112 (2015). https://doi.org/10.1007/s10240-014-0064-7

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  • DOI: https://doi.org/10.1007/s10240-014-0064-7

Keywords

  • Riemannian Manifold
  • Partial Regularity
  • Optimal Transport
  • Optimal Transportation
  • Smooth Density