Neuman and second boundary value problems for Hessian and Gauss curvature flows

Knut Smoczyk and Oliver Schnürer

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Submission date: 07. May. 2002
Pages: 34
published in: Annales de l'Institut Henri Poincaré / C, 20 (2003) 6, p. 1043-1073 
DOI number (of the published article): 10.1016/S0294-1449(03)00021-0
Bibtex
MSC-Numbers: 53C44, 35K20, 53C42
Keywords and phrases: geometric evolution, gauss curvature flow, second boundary value problem
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Abstract:
We consider the flow of a strictly convex hypersurface driven by the Gauss curvature. For the Neumann boundary value problem and for the second boundary value problem we show that such a flow exists for all times and converges eventually to a solution of the prescribed Gauss curvature equation. We also discuss oblique boundary value problems and flows for Hessian equations