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Partial regularity for optimal transport maps

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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Correspondence to Alessio Figalli.

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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