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

Author(s): Plácido Andrade
Journal: Proc. Amer. Math. Soc. 128 (2000), 1451-1457.
MSC (1991): Primary 53A10; Secondary 53C42
Posted: December 8, 1999
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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:

[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. 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).
[Rsb]: Rosenberg, H.; A complete embedded minimal surface in $\mathbb{R}^3$ of bounded curvature is proper; preprint.


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