Modified defect relations of the Gauss map and the total curvature of a complete minimal surface

TL;DR

This paper establishes conditions on the Gauss map's defect relations of a complete minimal surface to demonstrate that such surfaces have finite total curvature, contributing to the understanding of minimal surface geometry.

Contribution

It introduces new conditions on the modified defect relations of the Gauss map that imply finite total curvature for complete minimal surfaces.

Findings

Conditions on defect relations imply finite total curvature

Provides criteria linking Gauss map properties to surface curvature

Advances understanding of minimal surface geometry

Abstract

In this article, we propose some conditions on the modified defect relations of the Gauss map of a complete minimal surface $M$ to show that $M$ has finite total curvature.