A probabilistic method for gradient estimates of some geometric flows
Differential Geometry
2015-01-14 v2
Abstract
In general, gradient estimates are very important and necessary for deriving convergence results in different geometric flows, and most of them are obtained by analytic methods. In this paper, we will apply a stochastic approach to systematically give gradient estimates for some important geometric quantities under the Ricci flow, the mean curvature flow, the forced mean curvature flow and the Yamabe flow respectively. Our conclusion gives another example that probabilistic tools can be used to simplify proofs for some problems in geometric analysis.
Cite
@article{arxiv.1312.6484,
title = {A probabilistic method for gradient estimates of some geometric flows},
author = {Xin Chen and Li-Juan Cheng and Jing Mao},
journal= {arXiv preprint arXiv:1312.6484},
year = {2015}
}
Comments
22 pages. Minor revision to v1. Accepted for publication in Stochastic Processes and their Applications