Complete minimal surfaces in ℝ 3 with type Enneper end
Do Espirito Santo, Nedir
Annales de l'Institut Fourier, Tome 44 (1994), p. 525-557 / Harvested from Numdam
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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.

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.

@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},
     volume = {44},
     year = {1994},
     pages = {525-557},
     doi = {10.5802/aif.1408},
     mrnumber = {95h:53008},
     zbl = {0803.53006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/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) pp. 525-557. doi : 10.5802/aif.1408. http://gdmltest.u-ga.fr/item/AIF_1994__44_2_525_0/

[CG]C.C. Chen, F. Gacksttater, Elliptische und Hyperelliptische Funktionen und Vollständige Minimalflächen von Enneperschen Typ, Math. Ann., 259 (1982), 359-369. | MR 661204 | Zbl 0468.53008

[GP]A. Griffiths, Introduction to Algebraic Curves, Providence, AMS, 1989. | MR 1013999 | Zbl 0696.14012

[H]A. Huber, On subharmonic Functions and Differential Geometry in the Large, Comment Math. Helv., 32 (1957), 13-72. | MR 94452 | MR 20 #970 | Zbl 0080.15001

[JM]L. Jorge, W. Meeks, III The Topology of Complete Minimal Surfaces of Finite Total Gaussian Curvature, Topology, 22 (1983), 203-221. | MR 683761 | MR 84d:53006 | Zbl 0517.53008

[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. | MR 256278 | MR 41 #934 | Zbl 0209.52901