Equilibria for Anisotropic Surface Energies and the Gielis Formula

Miyuki Koiso¹ and Bennett Palmer²

¹Department of Mathematics, Nara Women's University, Nara 630-8506, Japan
²Department of Mathematics, Idaho State University, Pocatello, ID 83209, U.S.A.
*E-mail address: koiso@cc.nara-wu.ac.jp

(Received June 26, 2007; Accepted April 28, 2008)

Keywords: Anisotropic Mean Curvature, Gielis Formula, Wulff Shape, Delaunay Surface

Abstract. Anisotropic surface energies are used to model surface energies which depend on the direction of the surface normal. Equilibria of such energies are characterized as surfaces with constant anisotropic mean curvature. The surface of a crystal and certain interfaces of liquid crystals with an isotropic substrate give physical examples of such equilibria. We produce examples of surfaces having constant anisotropic mean curvature for anisotropic energy functionals having a Wulff shape based on the Gielis formula.