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Translating solutions for Gauß curvature flows with Neumann boundary condition
Oliver Schnürer and Hartmut Schwetlick
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.