Calculus of Variations and Geometric Measure Theory
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R. Grande

A stochastic representation for the solution of approximated mean curvature flow

created by grande on 14 May 2021

[BibTeX]

preprint

Inserted: 14 may 2021

Year: 2021

ArXiv: 2105.06393 PDF

Abstract:

The evolution by horizontal mean curvature flow (HMCF) is a partial differential equation in a sub-Riemannian setting with application in IT and neurogeometry (see Citti-Franceschiello-Sanguinetti-Sarti, 2016). 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 define 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 flow, generalizing the result of Dirr-Dragoni-von Renesse, 2010.

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