Reference : Coupling of Brownian motions and Perelman's L-functional
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Coupling of Brownian motions and Perelman's L-functional
Kuwada, Kazumasa mailto [Ochanomizu University > Department of Mathematics]
Philipowski, Robert mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Journal of Functional Analysis
Academic Press
Yes (verified by ORBilu)
[en] Ricci flow ; L-functional ; Brownian motion ; Coupling
[en] 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 their normalized L-distance is a supermartingale. As a corollary, we obtain the monotonicity of the transportation cost between two solutions of the heat equation in the case that the cost function is the composition of a concave non-decreasing function and the normalized L-distance. In particular, it provides a new proof of a recent result of Topping [P. Topping, L-optimal transportation for Ricci flow, J. Reine Angew. Math. 636 (2009) 93–122].

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