Un théorème d'unicité de l'hélicoïde

Eric Toubiana

Annales de l'institut Fourier (1988)

  • Volume: 38, Issue: 4, page 121-132
  • ISSN: 0373-0956

Abstract

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We show that a complete minimal surface embedded in R 3 / Z with finite total curvature which is homeomorphic to S 2 minus two points is the “hélicoïde”’.

How to cite

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Toubiana, Eric. "Un théorème d'unicité de l'hélicoïde." Annales de l'institut Fourier 38.4 (1988): 121-132. <http://eudml.org/doc/74811>.

@article{Toubiana1988,
abstract = {Nous montrons qu’une surface minimale complété, plongée dans $\{\bf R\}^ 3/\{\bf Z\}$, de courbure totale finie et homéomorphe a $S^ 2$ moins deux points est l’hélicoïde.},
author = {Toubiana, Eric},
journal = {Annales de l'institut Fourier},
keywords = {helicoid; minimal surface},
language = {fre},
number = {4},
pages = {121-132},
publisher = {Association des Annales de l'Institut Fourier},
title = {Un théorème d'unicité de l'hélicoïde},
url = {http://eudml.org/doc/74811},
volume = {38},
year = {1988},
}

TY - JOUR
AU - Toubiana, Eric
TI - Un théorème d'unicité de l'hélicoïde
JO - Annales de l'institut Fourier
PY - 1988
PB - Association des Annales de l'Institut Fourier
VL - 38
IS - 4
SP - 121
EP - 132
AB - Nous montrons qu’une surface minimale complété, plongée dans ${\bf R}^ 3/{\bf Z}$, de courbure totale finie et homéomorphe a $S^ 2$ moins deux points est l’hélicoïde.
LA - fre
KW - helicoid; minimal surface
UR - http://eudml.org/doc/74811
ER -

References

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  1. [1] L. JORGE, W. MEEKS, The topology of complete minimal surfaces of finite total Gaussian curvature. Topology, Vol. 22, n° 2 (1983), 203-221. Zbl0517.53008MR84d:53006
  2. [2] R. LANGEVIN, G. LEVITT, H. ROSENBERG, Complete minimal surfaces with long lines boundary. A paraître dans Duke Mathematical Journal. Zbl0637.53007
  3. [3] H. BLAINE LAWSON, Lectures on minimal submanifolds, Vol. 1, Math-lecture Series 9, Publish or Perish. Zbl0434.53006
  4. [4] R. OSSERMAN, A survey of minimal surfaces. Van Nostrand Reinhold Math. Studies, 25, 1969. Zbl0209.52901MR41 #934
  5. [5] R. OSSERMAN, Global properties of minimal surfaces in E3 and En, Annals of Math., Vol. 80 (1964), 340-364. Zbl0134.38502MR31 #3946
  6. [6] B. RIEMANN, Œuvres complètes, tome XIII des mémoires de la société royale de Goettinguen (1987), p. 305. 
  7. [7] E. TOUBIANA, Thèse de doctorat. 

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