Evolution by mean curvature flow in sub-Riemannian geometries:
A stochastic approach
Nicolas Dirr - Department of Mathematical Sciences, University of Bath, Bath, BA1 7AY, United Kingdom (email)
Abstract: We study evolution by horizontal mean curvature flow in sub- Riemannian geometries by using 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.
Keywords: Mean curvature flow, sub-Riemannian geometries, level set equation, stochastic processes and control.
Received: January 2009; Revised: August 2009; Published: December 2009.
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