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

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.

arXiv comment22 pages. the references and the introduction were changed. arXiv admin note: substantial text overlap with arXiv:1710.02023; text overlap with arXiv:1411.2730