Document Type

Article

Publication Date

2-8-2013

Publication Title

Journal of Functional Analysis

Abstract

We introduce a sub-Riemannian analogue of the Bence–Merriman–Osher algorithm (Merriman et al., 1992) and show that it leads to weak solutions of the horizontal mean curvature flow of graphs over sub-Riemannian Carnot groups. The proof follows the nonlinear semi-group theory approach originally introduced by L.C. Evans (1993) in the Euclidean setting and is based on new results on the relation between sub-Riemannian heat flows of characteristic functions of subgraphs and the horizontal mean curvature of the corresponding graphs.

Volume

264

Issue

8

First Page Number

1899

Last Page Number

1928

DOI

10.1016/j.jfa.2013.01.020

Version

Preprint

Publisher Statement

This is a pre-print of an article published in the Journal of Functional Analysis. The final authenticated version is available online at: https://doi.org/10.1016/j.jfa.2013.01.020.

Rights

Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.

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