Partial regularity for optimal transport maps

Guido De Philippis, Alessio Figalli

Research output: Contribution to journalArticle

Abstract

We prove that, for general cost functions on Rn, or for the cost d2/2 on a Riemannian manifold, optimal transport maps between smooth densities are always smooth outside a closed singular set of measure zero.

Original languageEnglish (US)
Pages (from-to)81-112
Number of pages32
JournalPublications Mathematiques de l'Institut des Hautes Etudes Scientifiques
Volume121
Issue number1
DOIs
StatePublished - Jun 27 2015

ASJC Scopus subject areas

  • Mathematics(all)

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