Methods and Applications of Analysis
Volume 15 (2008)
An Approximation Lemma about the Cut Locus, with Applications in Optimal Transport Theory
Pages: 149 – 154
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.
Cut locus; optimal transport; co-area formula
2010 Mathematics Subject Classification
35B65, 49Q20, 53C20