Interior gradient estimates for anisotropic mean-curvature flow

Julie Clutterbuck

Vol. 229 (2007), No. 1, 119–136

DOI: 10.2140/pjm.2007.229.119

Abstract

In this paper we consider the evolution of a graph-like hypersurface by anisotropic mean-curvature flow, under some restrictions on the anisotropic area integrand. We find interior estimates (in both time and space) on the gradient of such hypersurfaces, depending only on the height of the graph and the anisotropic area integrand.

Keywords

evolution equations, anisotropic mean curvature flow, gradient estimates

Mathematical Subject Classification 2000

Primary: 35K55, 53A07

Milestones

Received: 15 March 2005

Accepted: 17 August 2005

Published: 1 January 2007