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


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


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

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},

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 -


  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. 

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.