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.
Highlights
In Euclidean spaces, the motion by mean curvature flow of a hypersurface is a geometrical evolution such that the normal velocity at each point of the hypersurface is equal to the mean curvature at that point
We study evolution by horizontal mean curvature flow in subRiemannian 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
Summary
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