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Concerning the value distribution problem for generalized Gauss maps, we notonly generalize Fujimoto's theorem to complete space-like stationary surfacesin Minkowski spacetime, but also estimate the upper bound of the number ofexceptional values when the Gauss image lies in the graph of a rationalfunction f of degree m, showing a sharp contrast to Bernstein type results forminimal surfaces in 4-dimensional Euclidean space. Moreover, we introduce theconception of conjugate similarity on the special linear group to classify alldegenerate stationary surfaces (i.e. m=0 or 1), and establish several structuretheorems for complete stationary graphs in Minkowski spacetime from theviewpoint of the degeneracy of Gauss maps.

On complete space-like stationary surfaces in Minkowski spacetime with graphical Gauss image