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

Abstract

We study evolution by horizontal mean curvature flow in sub-Riemannian geometries by using stochastic approach to prove the existence ofa generalized evolution in these spaces. In particular we show that the valuefunction of suitable family of stochastic control problems solves in the viscositysense the level set equation for the evolution by horizontal mean curvature flow.