Evolution by mean curvature in sub-Riemannian geometries: A stochastic approach
Analysis of PDEs
2008-12-18 v1 Probability
Abstract
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
Cite
@article{arxiv.0812.3288,
title = {Evolution by mean curvature in sub-Riemannian geometries: A stochastic approach},
author = {Nicolas Dirr and Federica Dragoni and Max von Renesse},
journal= {arXiv preprint arXiv:0812.3288},
year = {2008}
}