Evolution by mean curvature in sub-Riemannian geometries: A stochastic   approach
  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. 
Nicolas Dirr, Federica Dragoni and Max von Renesse