Ramification and unicity theorems for Gauss maps of complete space-like stationary surfaces in four-dimensional Lorentz-Minkowski space

Abstract

In this paper, we investigate the value distribution properties for Gauss maps of space-like stationary surfaces in four-dimensional Lorentz-Minkowski space $\mathbb{R}^{3,1}$, focusing on aspects such as the number of totally ramified points and unicity properties. We not only obtain general conclusions similar to situations in four-dimensional Euclidean space, but also consider the space-like stationary surfaces with rational graphic Gauss image, which is an extension of degenerate space-like stationary surfaces.