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A probabilistic method for gradient estimates of some geometric flows

Author

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  • Chen, Xin
  • Cheng, Li-Juan
  • Mao, Jing

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.

Suggested Citation

  • Chen, Xin & Cheng, Li-Juan & Mao, Jing, 2015. "A probabilistic method for gradient estimates of some geometric flows," Stochastic Processes and their Applications, Elsevier, vol. 125(6), pages 2295-2315.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:6:p:2295-2315
    DOI: 10.1016/j.spa.2015.01.001
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    References listed on IDEAS

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    1. Arnaudon, Marc & Driver, Bruce K. & Thalmaier, Anton, 2007. "Gradient estimates for positive harmonic functions by stochastic analysis," Stochastic Processes and their Applications, Elsevier, vol. 117(2), pages 202-220, February.
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    1. Cheng, Li-Juan, 2014. "A probabilistic approach for gradient estimates on time-inhomogeneous manifolds," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 174-183.

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