A classification of minimal translation surfaces in Minkowski space

Abstract

Minimal surfaces are well known as a class of surfaces with vanishing mean curvature which minimize area within a given boundary configuration since 19th century. This fact was implicitly proved by Lagrange for nonparametric surfaces in 1760, and then by Meusnier in 1776 who used the analytic expression for the mean curvature. Mathematically, a minimal surface corresponds to the solution of a nonlinear partial differential equation. By solving some differential equations, in this paper we give a complete and explicit classification of minimal translation surfaces in an n-dimensional Minkowski space.