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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A wild minimal plane in $\mathbb{R}^3$


Author: Plácido Andrade
Journal: Proc. Amer. Math. Soc. 128 (2000), 1451-1457
MSC (1991): Primary 53A10; Secondary 53C42
Published electronically: December 8, 1999
MathSciNet review: 1664289
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Abstract | References | Similar Articles | Additional Information

Abstract: The main object of this article is to construct a complete minimal immersed plane in $\mathbb{R}^3$ whose closure has nonempty interior but it is not dense in the whole space. Furthermore, its Gaussian curvature is bounded.


References [Enhancements On Off] (What's this?)

  • [And] Andrade, P.; Enneper Immersions; Jorn. D'Ann. Math. vol LXXV, (1998), 121-134. CMP 99:04
  • [B-C] J. Lucas M. Barbosa and A. Gervasio Colares, Minimal surfaces in 𝑅³, Lecture Notes in Mathematics, vol. 1195, Springer-Verlag, Berlin, 1986. Translated from the Portuguese. MR 853728 (87j:53010)
  • [Jor] Jorge, L. P.; personal conversation.
  • [J-S] Howard Jenkins and James Serrin, Variational problems of minimal surface type. I, Arch. Rational mech. Anal. 12 (1963), 185–212. MR 0145194 (26 #2729)
  • [Law] Lawrence, J. D.; A Catalog of Special Plane Curves, Dover Publications Inc. (1972).
  • [Rsb] Rosenberg, H.; A complete embedded minimal surface in $\mathbb{R}^3$ of bounded curvature is proper; preprint.

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Additional Information

Plácido Andrade
Affiliation: Universidade Federal do Ceará, Departamento de Matemática, Campus do Pici Bloco 914, CEP 60.455-760 Fortaleza, CE, Brazil
Email: andrade@mat.ufc.br

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05323-X
PII: S 0002-9939(99)05323-X
Received by editor(s): June 23, 1998
Published electronically: December 8, 1999
Communicated by: Peter Li
Article copyright: © Copyright 2000 American Mathematical Society