Non-integrated defect relations for the Gauss map of a complete minimal surface with finite total curvature in $\mathbb R^m$

TL;DR

This paper establishes non-integrated defect relations for the Gauss map of complete minimal surfaces with finite total curvature in higher-dimensional Euclidean spaces, extending previous results to more complex target spaces.

Contribution

It extends earlier work on defect relations of the Gauss map to higher-dimensional targets for complete minimal surfaces with finite total curvature.

Findings

Derived new non-integrated defect relations for the Gauss map.

Extended previous results to higher-dimensional Euclidean spaces.

Provided a broader understanding of the Gauss map's value distribution.

Abstract

In this article, we give the non-integrated defect relations for the Gauss map of a complete minimal surface with finite total curvature in $\mathbb R^m.$ This is a continuation of previous work of Ha-Trao [J. Math. Anal. Appl., \textbf{430} (2015), 76-84.], which we extend here to targets of higher dimension.