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 value distribution properties for Gauss maps of space-like stationary surfaces in four-dimensional Lorentz-Minkowski space $R^{3,1}$, focusing on aspects such as the total weight of totally ramified values and unicity properties. We obtain not only general conclusions analogous to those in four-dimensional Euclidean space, but also results for space-like stationary surfaces with rational graphical Gauss image, which is an extension of degenerate space-like stationary surfaces.