The radial part of Brownian motion with respect to L-distance under Ricci flow

2012/11/15 by Cheng, Lijuan
#53C44 #58J65 #60J65 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1211.3626

Abstract

Let \g_t\_{t∈ [0,T)} be a family of complete time-depending Riemannian matrics on a manifold which evolves under backwards Ricci flow. The Itô formula is established for the L-distance of the g_t-Brownian motion to a fixed reference point (L-base). Furthermore, as an application, we construct a coupling by parallel displacement which yields a new proof of some results of Topping.

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