Partial Regularity for Optimal Transport Maps

Abstract

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

Topics

Cite this paper

@inproceedings{Philippis2014PartialRF, title={Partial Regularity for Optimal Transport Maps}, author={Guido De Philippis}, year={2014} }