Partial Regularity for optimal transport maps

Alessio Figalli; Guido De Philippis

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Partial Regularity for optimal transport maps

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arxiv 1209.5640 v2 pith:RTPDNLLB submitted 2012-09-25 math.AP

Guido De Philippis , Alessio Figalli This is my paper

classification math.AP

keywords costmapsoptimalsmoothtransportalwayscloseddensities

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abstract

We prove that, for general cost functions on $\mathbb{R}^n$, 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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