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

Dirr, Nicolas P. ORCID: https://orcid.org/0000-0003-3634-7367, Dragoni, Federica ORCID: https://orcid.org/0000-0001-6076-9725 and Von Renesse, Max 2010. Evolution by mean curvature flow in sub-Riemannian geometries: a stochastic approach. Communications on Pure and Applied Analysis 9 (2) , pp. 307-326. 10.3934/cpaa.2010.9.307

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Abstract

We study evolution by horizontal mean curvature flow in sub-Riemannian 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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Mean curvature flow, sub-Riemannian geometries, level set equation, stochastic processes and control
Publisher:	American Institute of Mathematical Sciences
ISSN:	1534-0392
Last Modified:	18 Oct 2022 13:13
URI:	https://orca.cardiff.ac.uk/id/eprint/13071

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