Value distribution for the Gauss maps of various classes of surfaces

TL;DR

This paper surveys recent advances in the value distribution theory of Gauss maps for various classes of immersed surfaces in space forms, highlighting geometric insights and unifying themes across different surface types.

Contribution

It provides a comprehensive overview of recent results and clarifies the geometric context for the value distribution properties of Gauss maps in multiple surface classes.

Findings

Summarizes key recent results in the field.

Connects geometric background with value distribution theory.

Highlights differences among surface classes.

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.