Construction de surfaces minimales en recollant des surfaces de Scherk

Martin Traizet

Annales de l'institut Fourier (1996)

  • Volume: 46, Issue: 5, page 1385-1442
  • ISSN: 0373-0956

Abstract

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We construct simply periodic minimal surfaces in euclidean 3-space by gluing together Scherk surfaces, using the techniques of Kapouleas.

How to cite

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Traizet, Martin. "Construction de surfaces minimales en recollant des surfaces de Scherk." Annales de l'institut Fourier 46.5 (1996): 1385-1442. <http://eudml.org/doc/75218>.

@article{Traizet1996,
abstract = {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.},
author = {Traizet, Martin},
journal = {Annales de l'institut Fourier},
keywords = {minimal surfaces; desingularization; Euclidean space; Scherk surfaces},
language = {fre},
number = {5},
pages = {1385-1442},
publisher = {Association des Annales de l'Institut Fourier},
title = {Construction de surfaces minimales en recollant des surfaces de Scherk},
url = {http://eudml.org/doc/75218},
volume = {46},
year = {1996},
}

TY - JOUR
AU - Traizet, Martin
TI - Construction de surfaces minimales en recollant des surfaces de Scherk
JO - Annales de l'institut Fourier
PY - 1996
PB - Association des Annales de l'Institut Fourier
VL - 46
IS - 5
SP - 1385
EP - 1442
AB - 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.
LA - fre
KW - minimal surfaces; desingularization; Euclidean space; Scherk surfaces
UR - http://eudml.org/doc/75218
ER -

References

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  1. [1] T. AUBIN, Non linear Analysis on Manifolds, Monge Ampere Equations, Springer Verlag, 1982. Zbl0512.53044
  2. [2] M.P. DO CARMO, Riemannian Geometry, Birkhäuser, 1992. 
  3. [3] S. GALLOT, D. HULIN, J. LAFONTAINE, Riemannian Geometry, second edition, Springer Verlag, 1990. Zbl0716.53001MR91j:53001
  4. [4] D. GILBARG and N.S. TRUDINGER, Elliptic Partial Differential Equations of Second Order, 2nd Edition, Springer Verlag, 1983. Zbl0562.35001MR86c:35035
  5. [5] N. KAPOULEAS, Complete constant mean curvature surfaces in euclidean three-space, Annals of Math., 131 (1990), 239-330. Zbl0699.53007MR93a:53007a
  6. [6] H. KARCHER, Embedded minimal surfaces derived from Scherk's examples, Manuscripta Math., 62 (1988), 83-114. Zbl0658.53006MR89i:53009
  7. [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. [8] H. KARCHER, The triply periodic surfaces of Alan Schoen and their constant mean curvature companions, Manuscripta Math., 64 (1989), 291-357. Zbl0687.53010MR90g:53010
  9. [9] H. KARCHER, Construction of higher genus embedded minimal surfaces, Geom. and Top. of Submanifolds III World Sc. (1990), 174-191. Zbl0737.53007MR96e:53012
  10. [10] W.H. MEEKS, H. ROSENBERG, The Geometry of Periodic Minimal Surfaces, Comment. Math. Helvetici, 68 (1993), 538-578. Zbl0807.53049MR95a:53011
  11. [11] H. ROSENBERG, Some recent developments in the theory of properly embedded minimal surfaces in ℝ3, Séminaire Bourbaki, n° 759 (1992). Zbl0789.53003MR93m:53008

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