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Gerd Dethloff; Pham Hoang Ha
Ramification of the Gauss map of complete minimal surfaces in ${\mathbb{R}}^3$ and ${\mathbb{R}}^4$ on annular ends
Annales de la faculté des sciences de Toulouse Sér. 6, 23 no. 4 (2014), p. 829-846, doi: 10.5802/afst.1426
Article PDF | Reviews MR 3270425 | Zbl 06374890

Résumé - Abstract

In this article, we study the ramification 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 ([4], [5]) and Ru ([13], [14]) for (the whole) complete minimal surfaces, thus we show that the restriction of the Gauss map to an annular end of such a complete minimal surface cannot have more branching (and in particular not avoid more values) than on the whole complete minimal surface. We thus give an improvement of the results on annular ends of complete minimal surfaces of Kao ([8]).

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