Contents Online
Methods and Applications of Analysis
Volume 15 (2008)
Number 2
An Approximation Lemma about the Cut Locus, with Applications in Optimal Transport Theory
Pages: 149 – 154
DOI: https://dx.doi.org/10.4310/MAA.2008.v15.n2.a3
Authors
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
Cut locus, optimal transport, co-area formula
2010 Mathematics Subject Classification
35B65, 49Q20, 53C20
Published 1 January 2008