Document Type

Article

Publication Date

6-6-2015

Publication Title

Nonlinear Analysis

Abstract

We consider (smooth) solutions of the mean curvature flow of graphs over bounded domains in a Lie group free up to step two (and not necessarily nilpotent), endowed with a one parameter family of Riemannian metrics σϵ collapsing to a subRiemannian metric σ0 as ϵ→0. We establish Ck,α estimates for this flow, that are uniform as ϵ→0 and as a consequence prove long time existence for the subRiemannian mean curvature flow of the graph. Our proof extend to the setting of every step two Carnot group (not necessarily free) and can be adapted following our previous work in Capogna et al. (2013) to the total variation flow.

Volume

126

First Page Number

437

Last Page Number

450

DOI

10.1016/j.na.2015.05.008

Version

Preprint

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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