Value distribution for the Gauss maps of various classes of surfaces

Abstract

We present in this article a survey of recent results in value distribution theory for the Gauss maps of several classes of immersed surfaces in space forms, for example, minimal surfaces in Euclidean $n$-space ($n$=3 or 4), improper affine spheres in the affine 3-space and flat surfaces in hyperbolic 3-space. In particular, we elucidate the geometric background of their results.

arXiv comment15 pages, review paper. arXiv admin note: text overlap with arXiv:1311.1931, arXiv:1205.4782, arXiv:1606.02376