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arXiv · 1209.5640

Partial Regularity for optimal transport maps

Guido De Philippis·Alessio Figalli
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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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Guido De Philippis, Alessio Figalli. 2018-06-05. Partial Regularity for optimal transport maps. https://arxiv.org/abs/1209.5640

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