Inserted: 28 apr 2008
Last Updated: 28 nov 2008
Journal: Methods Appl. Anal.
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