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2014 Mean Curvature Type Flow with Perpendicular Neumann Boundary Condition inside a Convex Cone
Fangcheng Guo, Guanghan Li, Chuanxi Wu
Abstr. Appl. Anal. 2014: 1-7 (2014). DOI: 10.1155/2014/315768

Abstract

We investigate the evolution of hypersurfaces with perpendicular Neumann boundary condition under mean curvature type flow, where the boundary manifold is a convex cone. We find that the volume enclosed by the cone and the evolving hypersurface is invariant. By maximal principle, we prove that the solutions of this flow exist for all time and converge to some part of a sphere exponentially as t tends to infinity.

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Fangcheng Guo. Guanghan Li. Chuanxi Wu. "Mean Curvature Type Flow with Perpendicular Neumann Boundary Condition inside a Convex Cone." Abstr. Appl. Anal. 2014 1 - 7, 2014. https://doi.org/10.1155/2014/315768

Information

Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07022152
MathSciNet: MR3240531
Digital Object Identifier: 10.1155/2014/315768

Rights: Copyright © 2014 Hindawi

Vol.2014 • 2014
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