Stable closed equilibria for anisotropic surface energies: Surfaces with edges

Bennett Palmer

doi:10.3934/jgm.2012.4.89

Article Contents

2012, Volume 4, Issue 1: 89-97. Doi: 10.3934/jgm.2012.4.89

This issue Previous Article Variational reduction of Lagrangian systems with general constraints Next Article Lagrangian dynamics of submanifolds. Relativistic mechanics

Stable closed equilibria for anisotropic surface energies: Surfaces with edges

Bennett Palmer^1,

1.
Department of Mathematics, Idaho State University, Pocatello , Idaho, 83209

Received: October 31, 2011

Revised: March 31, 2012

Published: February 2012

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Abstract

We study the stability of closed, not necessarily smooth, equilibrium surfaces of an anisotropic surface energy for which the Wulff shape is not necessarily smooth. We show that if the Cahn-Hoffman field can be extended continuously to the whole surface and if the surface is stable, then the surface is, up to rescaling, the Wulff shape.

Keywords:

Anisotropic mean curvature,
second variation.

Mathematics Subject Classification: Primary: 49Q10; Secondary: 53A015.

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References

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