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

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