Ramification and unicity theorems for the Gauss maps of complete space-like stationary surfaces in R3,1

In this paper, we investigate the value distribution properties of Gauss maps for space-like stationary surfaces in four-dimension Lorentz-Minkowski space R3,1, focusing on aspects such as the number of totally ramified points and unicity properties. Particularly, as an extension of degenerate space-like stationary surfaces, we consider the space-like stationary surfaces with Gauss maps G=(ψ₁, ψ₂) satisfying ψ₂=f(ψ₁), where f is a rational function of degree m. In this case, we proved the ramification theorem and the unicity theorem for Gauss maps ψ₁.