## JMI2013A-9 Non-convex anisotropic surface energy and zero mean curvature surfaces in the Lorentz-Minkowski space (pp.73-82)

Author(s)： Atsufumi Honda, Miyuki Koiso and Yasuhiro Tanaka

J. Math-for-Ind. **5A** (2013) 73-82.

- File： JMI2013A-9.pdf (569KB)

Abstract

An anisotropic surface energy functional is the integral of an energy ensity function over a surface. The energy density depends on the surface normal at each point. The usual area functional is a special case of such a functional. We study stationary surfaces of anisotropic surface energies in the euclidean three-space which are called anisotropic minimal surfaces. For any axisymmetric anisotropic surface energy, we show that, a surface is both a minimal surface and an anisotropic minimal surface if and only if it is a right helicoid. We also construct new examples of anisotropic minimal surfaces, which include zero mean curvature surfaces in the three-dimensional Lorentz-Minkowski space as special cases.

Keyword(s). mean curvature, anisotropic, minimal surface, zero mean curvature surface, Lorentz-Minkowski space, Wulff shape