A stochastic representation for the solution of approximated mean curvature flow

Abstract The evolution by horizontal mean curvature flow (HMCF) is a partial differential equation in sub-Riemannian setting with applications IT and neurogeometry [see Citti et al. (SIAM J Imag Sci 9(1):212–237, 2016)]. Unfortunately this difficult to study, since the normal not always well defined. To overcome problem Riemannian approximation was introduced. In article we obtain stochastic representation of solution approximated using will prove that it viscosity sense flow, generalizing result Dirr (Commun Pure Appl Math 9(2):307–326, 2010).