A wild minimal plane in $\mathbb {R}^3$
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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
- Andrade, P.; Enneper Immersions; Jorn. D’Ann. Math. vol LXXV, (1998), 121-134.
- J. Lucas M. Barbosa and A. Gervasio Colares, Minimal surfaces in $\textbf {R}{^3}$, Lecture Notes in Mathematics, vol. 1195, Springer-Verlag, Berlin, 1986. Translated from the Portuguese. MR 853728, DOI 10.1007/BFb0077105
- Jorge, L. P.; personal conversation.
- Howard Jenkins and James Serrin, Variational problems of minimal surface type. I, Arch. Rational mech. Anal. 12 (1963), 185–212. MR 0145194, DOI 10.1007/BF00281225
- Lawrence, J. D.; A Catalog of Special Plane Curves, Dover Publications Inc. (1972).
- Rosenberg, H.; A complete embedded minimal surface in $\mathbb {R}^3$ of bounded curvature is proper; preprint.
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
- Received by editor(s): June 23, 1998
- Published electronically: December 8, 1999
- Communicated by: Peter Li
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 1451-1457
- MSC (1991): Primary 53A10; Secondary 53C42
- DOI: https://doi.org/10.1090/S0002-9939-99-05323-X
- MathSciNet review: 1664289