On the asymptotic behavior of a complete bounded minimal surface in ℝ³

On the asymptotic behavior of a complete bounded minimal surface in $\mathbb {R}^3$
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by Francisco Martín and Santiago Morales PDF

Trans. Amer. Math. Soc. 356 (2004), 3985-3994 Request permission

In this paper we construct an example of a complete minimal disk which is properly immersed in a ball of $\mathbb {R}^3$.

References

D. Hoffman and W. H. Meeks III, The strong halfspace theorem for minimal surfaces, Invent. Math. 101 (1990), no. 2, 373–377. MR 1062966, DOI 10.1007/BF01231506
F. J. López, F. Martín, and S. Morales, Adding handles to Nadirashvili’s surfaces, J. Differential Geom. 60 (2002), no. 1, 155–175. MR 1924594, DOI 10.4310/jdg/1090351086
Francisco Martín and Santiago Morales, A complete bounded minimal cylinder in $\Bbb R^3$, Michigan Math. J. 47 (2000), no. 3, 499–514. MR 1813541, DOI 10.1307/mmj/1030132591
S. Morales, On the existence of a proper minimal surface in $\mathbb {R}^3$ with the conformal type of a disk. G.A.F.A., to appear.
Nikolai Nadirashvili, Hadamard’s and Calabi-Yau’s conjectures on negatively curved and minimal surfaces, Invent. Math. 126 (1996), no. 3, 457–465. MR 1419004, DOI 10.1007/s002220050106
Robert Osserman, A survey of minimal surfaces, 2nd ed., Dover Publications, Inc., New York, 1986. MR 852409
Frederico Xavier, Convex hulls of complete minimal surfaces, Math. Ann. 269 (1984), no. 2, 179–182. MR 759107, DOI 10.1007/BF01451417