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Mean Curvature Type Flow with Perpendicular Neumann Boundary Condition inside a Convex Cone

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  • Fangcheng Guo
  • Guanghan Li
  • Chuanxi Wu

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.

Suggested Citation

  • Fangcheng Guo & Guanghan Li & Chuanxi Wu, 2014. "Mean Curvature Type Flow with Perpendicular Neumann Boundary Condition inside a Convex Cone," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:315768
    DOI: 10.1155/2014/315768
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    References listed on IDEAS

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    1. Murray H. Protter & Hans F. Weinberger, 1984. "Maximum Principles in Differential Equations," Springer Books, Springer, number 978-1-4612-5282-5, October.
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