A version of Krust’s theorem for anisotropic minimal surfaces

Abstract

We generalize Krust’s theorem to an anisotropic setting by showing the following. If Σ \Sigma is an anisotropic minimal surface in an axially symmetric normed linear space which is a graph over a convex domain contained in a plane orthogonal to the axis of symmetry, then its conjugate anisotropic minimal surface must also be a graph.

We also generalize a reflection principle of Lawson relating symmetries of an anisotropic minimal surface with symmetries of its conjugate surface.