Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.
MiS Preprint
14/2002
Translating solutions for Gauß curvature flows with Neumann boundary condition
Oliver Schnürer and Hartmut Schwetlick
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.