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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: 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] Barbosa, J. L. and Colares, A. G.; Minimal Surfaces in $\mathbb{R}^3$; Lectures Notes in Math. $n^o$ 1195, Springer-Verlag, 1986. MR 87j:53010
  • [Jor] Jorge, L. P.; personal conversation.
  • [J-S] Jenkins, H., Serrin, J.; Variational problems of minimal surfaces, type I; Arch. Rat. Anal. 12 (1963), 185-212. MR 26:2729
  • [Law] Lawrence, J. D.; A Catalog of Special Plane Curves, Dover Publications Inc. (1972).
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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

Received by editor(s): June 23, 1998
Published electronically: December 8, 1999
Communicated by: Peter Li
Article copyright: © Copyright 2000 American Mathematical Society