Duke Mathematical Journal

The classification of complete minimal surfaces in R3 with total curvature greater than 8π

William H. Meeks, III

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Article information

Source
Duke Math. J., Volume 48, Number 3 (1981), 523-535.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1077314779

Digital Object Identifier
doi:10.1215/S0012-7094-81-04829-8

Mathematical Reviews number (MathSciNet)
MR630583

Zentralblatt MATH identifier
0472.53010

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

Citation

Meeks, III, William H. The classification of complete minimal surfaces in $\mathbf{R}^3$ with total curvature greater than $ - 8 \pi$. Duke Math. J. 48 (1981), no. 3, 523--535. doi:10.1215/S0012-7094-81-04829-8. https://projecteuclid.org/euclid.dmj/1077314779


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References

  • [1] C. C. Chen and P. A. Q. Simões, Superficies minimas do $\mathbf{R}^{n}$, Escola de geometria diferencial, Universidade Estadual de Campinas, São Paulo, Brazil, 1980.
  • [2] F. Gackstatter, Topics on minimal surfaces, Departamento de matemática, São Paulo, Brazil, 1980, USP.
  • [3] D. A. Hoffman and R. Osserman, The geometry of the generalized Gauss map, Mem. Amer. Math. Soc. 28 (1980), no. 236, iii+105.
  • [4] L. P. Jorge and W. H. Meeks III, The topology of complete minimal surfaces of finite total curvature, to appear in Topology.
  • [5] W. H. Meeks III, Lectures on Plateau's problem, IMPA, Rio de Janeiro, Brazil, 1978.
  • [6] W. H. Meeks III, The conformal structure and geometry of triply periodic minimal surfaces in $\mathbf{R}^{3}$, Thesis, University of California, Berkeley, 1976, (revised).
  • [7] W. H. Meeks III, A survey of the geometric results in the classical theory of minimal surfaces, Bol. Soc. Brasil. Mat. 12 (1981), no. 1, 29–86.
  • [8] III, W. H. Meeks, The conjugate surface construction of symmetric complete minimal surfaces of small finite total curvature, in preparation.
  • [9] R. Osserman, Global properties of minimal surfaces in $E\sp{3}$ and $E\sp{n}$, Ann. of Math. (2) 80 (1964), 340–364.