Calculus of Variations and Geometric Measure Theory

A. Figalli - C. Villani

An approximation lemma about the cut locus, with applications in optimal transport theory

created by figalli on 28 Apr 2008
modified on 28 Nov 2008


Accepted Paper

Inserted: 28 apr 2008
Last Updated: 28 nov 2008

Journal: Methods Appl. Anal.
Year: 2008


A path in a Riemannian manifold can be approximated by a path meeting only finitely many times the cut locus of a given point. The proof of this property uses recent works of Itoh-Tanaka and Li-Nirenberg about the differential structure of the cut locus. We present applications in the regularity theory of optimal transport.

Keywords: Optimal transport, regularity, cut locus, approximation