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Embedded minimal surfaces, computer graphics and elliptic functions

Part of the Lecture Notes in Mathematics book series (LNM,volume 1156)

Keywords

  • Riemann Surface
  • Minimal Surface
  • Dihedral Group
  • Total Curvature
  • Gaussian Image

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References

  1. J. Lucas M. Barbosa and A. Gervasio Colares, Exemplos de Superficies Minimas no R3, Fifth Differential Geometry Workshop, University of São Paulo, July 30–August 4, 1984.

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  2. C. Costa, Imersões minimas completas em R3 de genero um e curvatura total finita, Doctoral thesis, IMPA, Rio de Janeiro, Brasil, 1982. (Also in "Example of a complete minimal immersion in R3 of genus one and three embedded ends", to appear in Boletim da Sociedade Brasiliera Mathematica, 15, No.1)

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  3. D. Hoffman and W. Meeks III, A complete embedded minimal surface with genus one, three ends and finite total curvature. (preprint)

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  4. D. Hoffman and W. Meeks III, Complete embedded minimal surfaces of finite total curvature. Bull.A.M.S., January 1985.

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  5. D. Hoffman and W. Meeks III, to appear

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  6. D. Hoffman and R. Osserman, The geometry of the generalized Gauss map, Mem. Amer Math. Soc. No. 236, 1980.

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  7. L. Jorge and W. Meeks III, The topology of complete minimal surfaces of finite total Gaussian curvature, Topology, 22 No. 2, 203–221, 1983.

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  8. R. Osserman, Global properties of complete minimal surfaces in E3 and En, Ann. of Math., (2) 80, 340–364, 1964.

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  9. R. Schoen, Uniqueness, symmetry, and embeddedness of minimal surfaces, J. Diff. Geom. 18, 791–809, 1983.

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© 1985 Springer-Verlag

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Hoffman, D. (1985). Embedded minimal surfaces, computer graphics and elliptic functions. In: Ferus, D., Gardner, R.B., Helgason, S., Simon, U. (eds) Global Differential Geometry and Global Analysis 1984. Lecture Notes in Mathematics, vol 1156. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075092

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  • DOI: https://doi.org/10.1007/BFb0075092

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15994-0

  • Online ISBN: 978-3-540-39698-7

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