Construction de surfaces minimales en recollant des surfaces de Scherk
Annales de l'Institut Fourier, Volume 46 (1996) no. 5, p. 1385-1442
We construct simply periodic minimal surfaces in euclidean 3-space by gluing together Scherk surfaces, using the techniques of Kapouleas.
On construit des surfaces minimales simplement périodiques dans l’espace euclidien de dimension 3 en recollant des surfaces de Scherk et en utilisant les techniques de Kapouleas.
@article{AIF_1996__46_5_1385_0,
     author = {Traizet, Martin},
     title = {Construction de surfaces minimales en recollant des surfaces de Scherk},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {46},
     number = {5},
     year = {1996},
     pages = {1385-1442},
     doi = {10.5802/aif.1554},
     zbl = {0860.53004},
     mrnumber = {98g:53012},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_1996__46_5_1385_0}
}
Traizet, Martin. Construction de surfaces minimales en recollant des surfaces de Scherk. Annales de l'Institut Fourier, Volume 46 (1996) no. 5, pp. 1385-1442. doi : 10.5802/aif.1554. http://www.numdam.org/item/AIF_1996__46_5_1385_0/

[1] T. Aubin, Non linear Analysis on Manifolds, Monge Ampere Equations, Springer Verlag, 1982. | Zbl 0512.53044

[2] M.P. Do Carmo, Riemannian Geometry, Birkhäuser, 1992.

[3] S. Gallot, D. Hulin, J. Lafontaine, Riemannian Geometry, second edition, Springer Verlag, 1990. | MR 91j:53001 | Zbl 0716.53001

[4] D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd Edition, Springer Verlag, 1983. | MR 86c:35035 | Zbl 0562.35001

[5] N. Kapouleas, Complete constant mean curvature surfaces in euclidean three-space, Annals of Math., 131 (1990), 239-330. | MR 93a:53007a | Zbl 0699.53007

[6] H. Karcher, Embedded minimal surfaces derived from Scherk's examples, Manuscripta Math., 62 (1988), 83-114. | MR 89i:53009 | Zbl 0658.53006

[7] H. Karcher, Construction of Minimal Surfaces, Surveys in Geometry, University of Tokyo (1989), 1-96, et Lecture Notes n° 12, SFB256, Bonn (1989).

[8] H. Karcher, The triply periodic surfaces of Alan Schoen and their constant mean curvature companions, Manuscripta Math., 64 (1989), 291-357. | MR 90g:53010 | Zbl 0687.53010

[9] H. Karcher, Construction of higher genus embedded minimal surfaces, Geom. and Top. of Submanifolds III World Sc. (1990), 174-191. | MR 96e:53012 | Zbl 0737.53007

[10] W.H. Meeks, H. Rosenberg, The Geometry of Periodic Minimal Surfaces, Comment. Math. Helvetici, 68 (1993), 538-578. | MR 95a:53011 | Zbl 0807.53049

[11] H. Rosenberg, Some recent developments in the theory of properly embedded minimal surfaces in ℝ3, Séminaire Bourbaki, n° 759 (1992). | Numdam | MR 93m:53008 | Zbl 0789.53003