Accepted Paper

Inserted: 28 apr 2008
Last Updated: 28 nov 2008

Journal: Methods Appl. Anal.
Year: 2008

Abstract:

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

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• cutlocus.pdf