A stochastic representation for the solution of approximated mean curvature flow

Grande, Raffaele 2022. A stochastic representation for the solution of approximated mean curvature flow. Nonlinear Differential Equations and Applications 29 , 9. 10.1007/s00030-021-00740-5

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Abstract

The evolution by horizontal mean curvature flow (HMCF) is a partial differential equation in a sub-Riemannian setting with applications in IT and neurogeometry . Unfortunately this equation is difficult to study,since the horizontal normal is not always well defined. To overcome this problem the Riemannian approximation was introduced. In this article we obtain a stochastic representation of the solution of the approximated Riemannian mean curvature using the Riemannian approximation and we will prove that it is a solution in the viscosity sense of the approximated mean curvature ow, generalizing the result of Dirr,Dragoni, von Renesse, 2010.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Additional Information:	This article is licensed under a Creative Commons Attribution 4.0 International License
Publisher:	Springer Verlag (Germany)
ISSN:	1021-9722
Date of First Compliant Deposit:	12 January 2022
Date of Acceptance:	24 November 2021
Last Modified:	15 May 2023 00:22
URI:	https://orca.cardiff.ac.uk/id/eprint/145946

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