Stable closed equilibria for anisotropic surface energies: Surfaces with edges

TL;DR

This paper investigates the stability of closed equilibrium surfaces under anisotropic surface energies, demonstrating that stability implies the surface is a scaled Wulff shape, even with non-smooth surfaces and edges.

Contribution

It extends stability analysis to non-smooth surfaces with edges and shows that stable equilibria are essentially scaled Wulff shapes under certain conditions.

Findings

Stable equilibrium surfaces are scaled Wulff shapes.

Continuity of the Cahn Hoffman field is crucial for stability.

Results apply to surfaces with edges and non-smooth features.

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.