A probabilistic method for gradient estimates of some geometric flows

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:125

Article

Chen, Xin¹  Cheng, Li-Juan²  Mao, Jing³ 

[1] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China

[2] Zhejiang Univ Technol, Dept Appl Math, Hangzhou 310023, Zhejiang, Peoples R China

[3] Harbin Inst Technol Weihai, Dept Math, Weihai 264209, Peoples R China

关键词: Brownian motion;    Local martingales;    Gradient estimates;    Time-changing metric;    Geometric flows;   

DOI  :  10.1016/j.spa.2015.01.001

来源: Elsevier

【 摘 要 】

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. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free