Journal of Differential Geometry

A complete embedded minimal surface in ${\bf R}\sp 3$ with genus one and three ends

David A. Hoffman and William Meeks, III

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Article information

Source
J. Differential Geom. Volume 21, Number 1 (1985), 109-127.

Dates
First available in Project Euclid: 26 June 2008

Permanent link to this document
http://projecteuclid.org/euclid.jdg/1214439467

Mathematical Reviews number (MathSciNet)
MR806705

Zentralblatt MATH identifier
0604.53002

Subjects
Primary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]
Secondary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]

Citation

Hoffman, David A.; Meeks, III, William. A complete embedded minimal surface in ${\bf R}\sp 3$ with genus one and three ends. J. Differential Geom. 21 (1985), no. 1, 109--127. http://projecteuclid.org/euclid.jdg/1214439467.


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References

  • [1] M. Abramovitz and I. Stegun, eds., Handbook of mathematical functions, Nat. Bureau Standards, Applied Math. Series, June, 1964, Chapter 18.
  • [2] D. Hoffman and W. H. Meeks, III, Complete embedded minimal surfaces of finite total curvature, Bull. Amer. Math. Soc. (N. S.), 1985, Vol. 12, 1,(January 1985) 134-135.
  • [3] C. Costa, Imersoes minimus completas em R3 de genero um e curatura total finita, Doctoral thesis, IMPA, Rio de Janeiro, Brasil, 1982 (Bol. Soc. Brasil. Mat., Vol. 15, No. 1 as "Example of a complete minimal immersion in R3 of genus one and three embedded ends"), to appear.
  • [4] D. Hoffman and R. Osserman, The geometry of the generalized Gauss map, Mem. Amer. Math. Soc, No. 236, 1980.
  • [5] L. Jorge and W. Meeks, III, The topology of complete minimal surfaces of finite total Gaussian curvature, Topology 22 (1983) 203-221.
  • [6] R. Osserman, Global properties of complete minimal surfaces in E3 and E", Ann. of Math. (2) 80 (1964) 340-364.
  • [7] R. Schoen, Uniqueness, symmetry, and embeddedness of minimal surfaces, J. Differential Geometry 18 (1983) 791-809.