A probabilistic method for gradient estimates of some geometric flows

Xin Chen, Li-Juan Cheng and Jing Mao

Stochastic Processes and their Applications, 2015, vol. 125, issue 6, 2295-2315

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.

Keywords: Brownian motion; Local martingales; Gradient estimates; Time-changing metric; Geometric flows (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:125:y:2015:i:6:p:2295-2315

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DOI: 10.1016/j.spa.2015.01.001

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