no. 2
Complete minimal surfaces in ℝ 3 with type Enneper end
Annales de l'Institut Fourier, Tome 44 (1994) no. 2, pp. 525-557

We show that there exists a complete minimal surface immersed into ℝ 3 which is conformally equivalent to a compact hyperelliptic Riemann surface of genus three minus one point. The end of the surface is of Enneper type and its total curvature is -16π.

Nous montrons l’existence d’une surface minimale complète dans l’espace ℝ 3 , conformément équivalente à une surface de Riemann hyperelliptique compacte de genre trois moins un point; son bout est de type Enneper et sa courbure totale est -16π.

@article{AIF_1994__44_2_525_0,
     author = {Do Espirito Santo, Nedir},
     title = {Complete minimal surfaces in ${\mathbb {R}}^3$ with type {Enneper} end},
     journal = {Annales de l'Institut Fourier},
     pages = {525--557},
     year = {1994},
     publisher = {Association des Annales de l'Institut Fourier},
     volume = {44},
     number = {2},
     doi = {10.5802/aif.1408},
     mrnumber = {95h:53008},
     zbl = {0803.53006},
     language = {en},
     url = {https://www.numdam.org/articles/10.5802/aif.1408/}
}
TY  - JOUR
AU  - Do Espirito Santo, Nedir
TI  - Complete minimal surfaces in ${\mathbb {R}}^3$ with type Enneper end
JO  - Annales de l'Institut Fourier
PY  - 1994
SP  - 525
EP  - 557
VL  - 44
IS  - 2
PB  - Association des Annales de l'Institut Fourier
UR  - https://www.numdam.org/articles/10.5802/aif.1408/
DO  - 10.5802/aif.1408
LA  - en
ID  - AIF_1994__44_2_525_0
ER  - 
%0 Journal Article
%A Do Espirito Santo, Nedir
%T Complete minimal surfaces in ${\mathbb {R}}^3$ with type Enneper end
%J Annales de l'Institut Fourier
%D 1994
%P 525-557
%V 44
%N 2
%I Association des Annales de l'Institut Fourier
%U https://www.numdam.org/articles/10.5802/aif.1408/
%R 10.5802/aif.1408
%G en
%F AIF_1994__44_2_525_0
Do Espirito Santo, Nedir. Complete minimal surfaces in ${\mathbb {R}}^3$ with type Enneper end. Annales de l'Institut Fourier, Tome 44 (1994) no. 2, pp. 525-557. doi: 10.5802/aif.1408

[CG]C.C. Chen, F. Gacksttater, Elliptische und Hyperelliptische Funktionen und Vollständige Minimalflächen von Enneperschen Typ, Math. Ann., 259 (1982), 359-369. | Zbl | MR | EuDML

[GP]A. Griffiths, Introduction to Algebraic Curves, Providence, AMS, 1989. | MR | Zbl

[H]A. Huber, On subharmonic Functions and Differential Geometry in the Large, Comment Math. Helv., 32 (1957), 13-72. | Zbl | MR | EuDML

[JM]L. Jorge, W. Meeks, III The Topology of Complete Minimal Surfaces of Finite Total Gaussian Curvature, Topology, 22 (1983), 203-221. | Zbl | MR

[K]H. Karcher, Construction of Minimal Surfaces, Surveys in Geometry, University of Tokyo 1989, p. 1-96, and Lecture Notes 12, SFB256, Bonn, 1989.

[O]R. Osserman, A Survey of Minimal Surfaces, van Nostrand Reinhold Company, 1969. | Zbl | MR

Cité par Sources :