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We study the phenomenon of evolution by horizontal mean curvature flow insub-Riemannian geometries. We use a stochastic approach to prove the existenceof a generalized evolution in these spaces. In particular we show that thevalue function of suitable family of stochastic control problems solves in theviscosity sense the level set equation for the evolution by horizontal meancurvature flow.

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