Modified defect relations of the Gauss map and the total curvature of a complete minimal surface. (English) Zbl 1380.53015
Summary: 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.
MSC:
| 53A10 | Minimal surfaces in differential geometry, surfaces with prescribed mean curvature |
| 53C42 | Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) |
| 30D35 | Value distribution of meromorphic functions of one complex variable, Nevanlinna theory |
| 32H30 | Value distribution theory in higher dimensions |
Keywords:
minimal surface; Gauss map; modified defect relation; value distribution theory; total curvatureReferences:
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