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MiS Preprint

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.

MSC Codes:
53C44, 35K20, 53C42
fully nonlinear, curvature flows

Related publications

2004 Repository Open Access
Oliver C. Schnürer and Hartmut R. Schwetlick

Translating solutions for Gauss curvature flows with Neumann boundary conditions

In: Pacific journal of mathematics, 213 (2004) 1, pp. 89-109