The radial part of Brownian motion with respect to $\mathcal{L}$-distance under Ricci flow

Lijuan Cheng

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arXiv · 1211.3626

The radial part of Brownian motion with respect to $\mathcal{L}$-distance under Ricci flow

Lijuan Cheng

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Abstract

Let $\{g_t\}_{t\in [0,T)}$ 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 $\mathcal{L}$-distance of the $g_t$-Brownian motion to a fixed reference point ($\mathcal{L}$-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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Lijuan Cheng. 2013-06-20. The radial part of Brownian motion with respect to $\mathcal{L}$-distance under Ricci flow. https://arxiv.org/abs/1211.3626

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