Calculus of Variations and Geometric Measure Theory

G. De Philippis - A. Figalli

Partial Regularity for optimal transport maps

created by dephilipp on 25 Sep 2012
modified on 31 May 2018


Accepted Paper

Inserted: 25 sep 2012
Last Updated: 31 may 2018

Journal: Publ. Math. Inst. Hautes √Čtudes Sci.
Year: 2014

ArXiv: 1209.5640 PDF


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.