Translating solutions for Gauß curvature flows with Neumann boundary condition
Oliver Schnürer and Hartmut Schwetlick
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Submission date: 19. Feb. 2002 (revised version: February 2003)
published in: Pacific journal of mathematics, 213 (2004) 1, p. 89-109
DOI number (of the published article): 10.2140/pjm.2004.213.89
MSC-Numbers: 53C44, 35K20, 53C42
Keywords and phrases: fully nonlinear, curvature flows
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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.