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

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.

arXiv commentarXiv admin note: text overlap with arXiv:0910.1730, arXiv:1007.1400 by other authors

References in corpus (2)

• Ricci flow with surgery on three-manifolds
• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds