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Translating solutions for Gauss curvature flows with Neumann boundary conditions

Oliver C. Schnuerer·Hartmut R. Schwetlick
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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.

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Oliver C. Schnuerer, Hartmut R. Schwetlick. 2003-02-27. Translating solutions for Gauss curvature flows with Neumann boundary conditions. https://arxiv.org/abs/math/0302345

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