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June 2008 An Approximation Lemma about the Cut Locus, with Applications in Optimal Transport Theory
Alessio Figalli, Cedric Villani
Methods Appl. Anal. 15(2): 149-154 (June 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.

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Alessio Figalli. Cedric Villani. "An Approximation Lemma about the Cut Locus, with Applications in Optimal Transport Theory." Methods Appl. Anal. 15 (2) 149 - 154, June 2008.

Information

Published: June 2008
First available in Project Euclid: 13 February 2009

zbMATH: 1172.53022
MathSciNet: MR2481676

Subjects:
Primary: 35B65, 49Q20, 53C20

Rights: Copyright © 2008 International Press of Boston

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Vol.15 • No. 2 • June 2008
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