Evolution by mean curvature flow in sub-Riemannian geometries: a stochastic approach

Nicolas Dirr, Federica Dragoni, and Max von Renesse

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Submission date: 20. Oct. 2008
Pages: 31
published in: Communications on pure and applied analysis, 9 (2010) 2, p. 307-326 
DOI number (of the published article): 10.3934/cpaa.2010.9.307
Bibtex
MSC-Numbers: 35D05
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Abstract:
We study the phenomenon of evolution by horizontal mean curvature flow in sub-Riemannian geometries. We use a stochastic approach to prove the existence of a generalized evolution in these spaces.In particular we show that the value function of suitable family of stochastic control problems solves in the viscosity sense the level set equation for the evolution by horizontal mean curvature flow.