Translating solutions for Gaußcurvature flows with Neumann boundary conditions

Oliver C. Schnürer and Hartmut R. Schwetlick

Vol. 213 (2004), No. 1, 89–109

DOI: 10.2140/pjm.2004.213.89

Abstract

We consider strictly convex hypersurfaces which are evolving by the non-parametric logarithmic Gauß curvature flow subject to a Neumann boundary condition. Solutions are shown to converge smoothly to hypersurfaces moving by translation. In particular, for bounded domains we prove that convex functions with prescribed normal derivative satisfy a uniform oscillation estimate.

Milestones

Received: 26 August 2002

Published: 1 January 2004