In this article, we study the ramification of the Gauss map of complete minimal surfaces in and 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]).
Dans ce travail nous obtenons des théorèmes de ramification de l’application de Gauss de certaines classes de surfaces minimales complètes dans et .
@article{AFST_2014_6_23_4_829_0,
author = {Gerd Dethloff and Pham Hoang Ha},
title = {Ramification of the {Gauss} map of complete minimal surfaces in ${\mathbb{R}}^3$ and ${\mathbb{R}}^4$ on annular ends},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {829--846},
publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
address = {Toulouse},
volume = {Ser. 6, 23},
number = {4},
year = {2014},
doi = {10.5802/afst.1426},
mrnumber = {3270425},
zbl = {06374890},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1426/}
}
TY - JOUR
AU - Gerd Dethloff
AU - Pham Hoang Ha
TI - Ramification of the Gauss map of complete minimal surfaces in ${\mathbb{R}}^3$ and ${\mathbb{R}}^4$ on annular ends
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 2014
SP - 829
EP - 846
VL - 23
IS - 4
PB - Université Paul Sabatier, Institut de Mathématiques
PP - Toulouse
UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1426/
DO - 10.5802/afst.1426
LA - en
ID - AFST_2014_6_23_4_829_0
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%D 2014
%P 829-846
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%N 4
%I Université Paul Sabatier, Institut de Mathématiques
%C Toulouse
%U https://afst.centre-mersenne.org/articles/10.5802/afst.1426/
%R 10.5802/afst.1426
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%F AFST_2014_6_23_4_829_0
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 : Mathématiques, Serie 6, Volume 23 (2014) no. 4, pp. 829-846. doi : 10.5802/afst.1426. https://afst.centre-mersenne.org/articles/10.5802/afst.1426/
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