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Guo, Fangcheng; Li, Guanghan; Wu, Chuanxi

Mean curvature type flow with perpendicular Neumann boundary condition inside a convex cone. (English) Zbl 1476.53112

Abstr. Appl. Anal. 2014, Article ID 315768, 7 p. (2014).
Summary: 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.

MSC:

53E10 Flows related to mean curvature

Keywords:

convex cone; volume; evolving hypersurface is invariant; maximum principle
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\textit{F. Guo} et al., Abstr. Appl. Anal. 2014, Article ID 315768, 7 p. (2014; Zbl 1476.53112)
Full Text: DOI

References:

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