Duke Mathematical Journal

A complete minimal Klein bottle in 3

Francisco J. López

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Duke Math. J., Volume 71, Number 1 (1993), 23-30.

First available in Project Euclid: 20 February 2004

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]


López, Francisco J. A complete minimal Klein bottle in $\mathbb{R}^3$. Duke Math. J. 71 (1993), no. 1, 23--30. doi:10.1215/S0012-7094-93-07102-5. https://projecteuclid.org/euclid.dmj/1077289835

Export citation


  • [Ba] A. A. Barros, Complete nonorientable minimal surfaces in $\mathbbR^3$ with finite total curvature, An. Acad. Brasil, Ciênc. 59 (1987), 141–143.
  • [Bl] D. Bloss, Elliptische Funktionen und vollständige Minimalflächen, thesis, Freien Univ. Berlin, Berlin, 1989.
  • [CG] C. C. Chen and F. Gackstatter, Elliptic and hyperelliptic functions and complete minimal surfaces with handles, vol. 27, Instituto de Matematica e Estatistica, Universidade de Sao Paulo, Brazil, 1981.
  • [FK] H. M. Farkas and I. Kra, Riemann Surfaces, Graduate Texts in Math., vol. 71, Springer-Verlag, Berlin, 1980.
  • [I1] T. Ishihara, Complete Möbius strips minimally immersed in $\mathbbR^3$, Proc. Amer. Math. Soc. 107 (1989), no. 3, 803–806.
  • [I2] T. Ishihara, Complete nonorientable minimal surfaces in $\mathbbR^3$, Trans. Amer. Math. Soc. 333 (1992), no. 2, 889–901.
  • [JM] L. Jorge and W. H. Meeks, The topology of complete minimal surfaces of finite total Gaussian curvature, Topology 22 (1983), no. 2, 203–221.
  • [K1] R. Kusner, Conformal geometry and complete minimal surfaces, Bull. Amer. Math. Soc. 17 (1987), no. 2, 291–295.
  • [K2] R. Kusner, Global geometry of extremal surfaces, dissertation, Univ. of California, Berkeley, 1988.
  • [L] F. J. Lopez, The classification of complete minimal surfaces with total curvature greater than $-12\pi$, Trans. Amer. Math. Soc. 334 (1992), no. 1, 49–74.
  • [LR] F. J. Lopez and A. Ros, On embedded complete minimal surfaces of genus zero, J. Differential Geom. 33 (1991), no. 1, 293–300.
  • [M] W. H. Meeks, The classification of complete minimal surfaces in $\mathbbR^3$ with total curvature greater than $-8\pi$, Duke Math. J. 48 (1981), no. 3, 523–535.
  • [Ol] M. E. G. G. de Oliveira, Some new examples of nonorientable minimal surfaces, Proc. Amer. Math. Soc. 98 (1986), no. 4, 629–636.
  • [Os] R. Osserman, A Survey of Minimal Surfaces, 2nd ed., Dover Publications, New York, 1986.
  • [S] N. Schmitt, Minimal surfaces with flat ends, dissertation, Univ. of Mass., Amherst, 1993.
  • [Sp] M. Spivak, A Comprehensive Introduction to Differential Geometry, Volume 3, Publish or Perish, Boston, Mass., 1975.
  • [T] E. Toubiana, Surfaces minimales non orientables de genre quelconque, preprint.