Calculus of Variations and Geometric Measure Theory
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N. Dirr - F. Dragoni - M. von Renesse

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

created by dragoni on 13 Oct 2008
modified on 02 Jul 2019


Published Paper

Inserted: 13 oct 2008
Last Updated: 2 jul 2019

Journal: Commun. Pure Appl. Anal.
Volume: 9
Number: 2
Pages: 307-326
Year: 2009


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.

Keywords: Mean Curvature Flows, sub-Riemaninan, Carnot group, Heisenberg group


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