On the asymptotic behavior of a complete bounded minimal surface in $\mathbb {R}^3$
Authors:
Francisco Martín and Santiago Morales
Journal:
Trans. Amer. Math. Soc. 356 (2004), 3985-3994
MSC (2000):
Primary 53A10; Secondary 49Q05, 49Q10, 53C42
DOI:
https://doi.org/10.1090/S0002-9947-04-03451-8
Published electronically:
January 23, 2004
MathSciNet review:
2058515
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Abstract | References | Similar Articles | Additional Information
Abstract: In this paper we construct an example of a complete minimal disk which is properly immersed in a ball of $\mathbb {R}^3$.
- 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 https://doi.org/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
- 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 https://doi.org/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 https://doi.org/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 https://doi.org/10.1007/BF01451417
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Additional Information
Francisco Martín
Affiliation:
Departamento de Geometría y Topología, Universidad de Granada, 18071 Granada, Spain
MR Author ID:
631746
ORCID:
0000-0002-5532-7567
Email:
fmartin@ugr.es
Santiago Morales
Affiliation:
Departamento de Geometría y Topología, Universidad de Granada, 18071 Granada, Spain
MR Author ID:
631746
ORCID:
0000-0002-5532-7567
Email:
santimo@ugr.es
Keywords:
Complete bounded minimal surfaces,
proper minimal immersions
Received by editor(s):
February 4, 2003
Received by editor(s) in revised form:
June 20, 2003
Published electronically:
January 23, 2004
Additional Notes:
This research was partially supported by MCYT-FEDER Grant no. BFM2001-3489
Article copyright:
© Copyright 2004
American Mathematical Society
