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}, pages = {1385--1442}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {46}, number = {5}, year = {1996}, doi = {10.5802/aif.1554}, mrnumber = {98g:53012}, zbl = {0860.53004}, language = {fr}, url = {http://archive.numdam.org/articles/10.5802/aif.1554/} }
TY - JOUR AU - Traizet, Martin TI - Construction de surfaces minimales en recollant des surfaces de Scherk JO - Annales de l'Institut Fourier PY - 1996 SP - 1385 EP - 1442 VL - 46 IS - 5 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.1554/ DO - 10.5802/aif.1554 LA - fr ID - AIF_1996__46_5_1385_0 ER -
%0 Journal Article %A Traizet, Martin %T Construction de surfaces minimales en recollant des surfaces de Scherk %J Annales de l'Institut Fourier %D 1996 %P 1385-1442 %V 46 %N 5 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.1554/ %R 10.5802/aif.1554 %G fr %F 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://archive.numdam.org/articles/10.5802/aif.1554/
[1] Non linear Analysis on Manifolds, Monge Ampere Equations, Springer Verlag, 1982. | Zbl
,[2] Riemannian Geometry, Birkhäuser, 1992.
,[3] Riemannian Geometry, second edition, Springer Verlag, 1990. | MR | Zbl
, , ,[4] Elliptic Partial Differential Equations of Second Order, 2nd Edition, Springer Verlag, 1983. | MR | Zbl
and ,[5] Complete constant mean curvature surfaces in euclidean three-space, Annals of Math., 131 (1990), 239-330. | MR | Zbl
,[6] Embedded minimal surfaces derived from Scherk's examples, Manuscripta Math., 62 (1988), 83-114. | MR | Zbl
,[7] Construction of Minimal Surfaces, Surveys in Geometry, University of Tokyo (1989), 1-96, et Lecture Notes n° 12, SFB256, Bonn (1989).
,[8] The triply periodic surfaces of Alan Schoen and their constant mean curvature companions, Manuscripta Math., 64 (1989), 291-357. | MR | Zbl
,[9] Construction of higher genus embedded minimal surfaces, Geom. and Top. of Submanifolds III World Sc. (1990), 174-191. | MR | Zbl
,[10] The Geometry of Periodic Minimal Surfaces, Comment. Math. Helvetici, 68 (1993), 538-578. | MR | Zbl
, ,[11] Some recent developments in the theory of properly embedded minimal surfaces in ℝ3, Séminaire Bourbaki, n° 759 (1992). | Numdam | MR | Zbl
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