Complete minimal surfaces of arbitrary genus in a slab of 3
Annales de l'Institut Fourier, Tome 46 (1996) no. 2, pp. 535-546.

Dans cet article nous construisons des surfaces minimales complètes de genre arbitraire dans 3 ayant un, deux, trois et quatre bouts respectivement et, de plus, les surfaces sont situées entre deux plans parallèles de 3 .

In this paper we construct complete minimal surfaces of arbitrary genus in 3 with one, two, three and four ends respectively. Furthermore the surfaces lie between two parallel planes of 3 .

@article{AIF_1996__46_2_535_0,
     author = {Costa, Celso J. and Sim\"oes, Plinio A. Q.},
     title = {Complete minimal surfaces of arbitrary genus in a slab of ${\mathbb {R}}^3$},
     journal = {Annales de l'Institut Fourier},
     pages = {535--546},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {46},
     number = {2},
     year = {1996},
     doi = {10.5802/aif.1523},
     mrnumber = {97e:53015},
     zbl = {0853.53005},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.1523/}
}
TY  - JOUR
AU  - Costa, Celso J.
AU  - Simöes, Plinio A. Q.
TI  - Complete minimal surfaces of arbitrary genus in a slab of ${\mathbb {R}}^3$
JO  - Annales de l'Institut Fourier
PY  - 1996
SP  - 535
EP  - 546
VL  - 46
IS  - 2
PB  - Association des Annales de l’institut Fourier
UR  - http://www.numdam.org/articles/10.5802/aif.1523/
DO  - 10.5802/aif.1523
LA  - en
ID  - AIF_1996__46_2_535_0
ER  - 
%0 Journal Article
%A Costa, Celso J.
%A Simöes, Plinio A. Q.
%T Complete minimal surfaces of arbitrary genus in a slab of ${\mathbb {R}}^3$
%J Annales de l'Institut Fourier
%D 1996
%P 535-546
%V 46
%N 2
%I Association des Annales de l’institut Fourier
%U http://www.numdam.org/articles/10.5802/aif.1523/
%R 10.5802/aif.1523
%G en
%F AIF_1996__46_2_535_0
Costa, Celso J.; Simöes, Plinio A. Q. Complete minimal surfaces of arbitrary genus in a slab of ${\mathbb {R}}^3$. Annales de l'Institut Fourier, Tome 46 (1996) no. 2, pp. 535-546. doi : 10.5802/aif.1523. http://www.numdam.org/articles/10.5802/aif.1523/

[1] F.F. Brito, Power series with Hadamard gaps and hyperbolic complete minimal surfaces, Duke Math. Journal, 68 (1993), 297-300. | MR | Zbl

[2] L.P.M. Jorge and F. Xavier, A complete minimal surfaces in R3 between two parallel planes, Ann. Math., 112 (1980), 203-206. | MR | Zbl

[3] F.R. Lopez, A non orientable complete minimal surfaces in R3 between two parallel planes, Proc. Am. Math. Soc., 103 (1988). | MR | Zbl

[4] R. Osserman, A survey of minimal surfaces, Van Nostrand, New York, 1969. | MR | Zbl

[5] H. Rosenberg and E. Toubiana, A cylindrical type complete minimal surfaces in a slab of R3, Bull. Sc. Math., III (1987), 241-245. | MR | Zbl

[6] A. Zygmund, Trigonometric series, Cambridge University Press, New York, 1968.

Cité par Sources :