Modified defect relations of the Gauss map of complete minimal surfaces on annular ends

Pham Hoang Ha; Nguyen Hoang Trang

Modified defect relations of the Gauss map of complete minimal surfaces on annular ends

Differential Geometry 2014-08-14 v1

Authors: Pham Hoang Ha , Nguyen Hoang Trang

Abstract

In this article, we study the modified defect relations of the Gauss map of complete minimal surfaces in $\mathbb R^3$ and $\mathbb R^4$ on annular ends. We obtain results which are similar to the ones obtained by Fujimoto~[J. Differential Geometry \textbf{29} (1989), 245-262] for (the whole) complete minimal surfaces. We thus give some improvements of the previous results for the Gauss maps of complete minimal surfaces restricted on annular ends.

Keywords

gauss map complete minimal surfaces annular ends defect relations modified defect differential geometry

Cite

@article{arxiv.1408.3075,
  title  = {Modified defect relations of the Gauss map of complete minimal surfaces on annular ends},
  author = {Pham Hoang Ha and Nguyen Hoang Trang},
  journal= {arXiv preprint arXiv:1408.3075},
  year   = {2014}
}

Comments

18 pages. arXiv admin note: substantial text overlap with arXiv:1304.7065

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