Coupling of Brownian motions and Perelman's L-functional
Probability
2010-07-09 v1 Differential Geometry
Abstract
We show that on a manifold whose Riemannian metric evolves under backwards Ricci flow two Brownian motions can be coupled in such a way that the expectation of their normalized L-distance is non-increasing. As an immediate corollary we obtain a new proof of a recent result of Topping (J. reine angew. Math. 636 (2009), 93-122), namely that the normalized L-transportation cost between two solutions of the heat equation is non-increasing as well.
Keywords
Cite
@article{arxiv.1007.1400,
title = {Coupling of Brownian motions and Perelman's L-functional},
author = {Kazumasa Kuwada and Robert Philipowski},
journal= {arXiv preprint arXiv:1007.1400},
year = {2010}
}
Comments
20 pages