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Transactions of the American Mathematical Society
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On the asymptotic behavior of a complete bounded minimal surface in $\mathbb{R} ^3$

Author(s): Francisco Martín; Santiago Morales
Journal: Trans. Amer. Math. Soc. 356 (2004), 3985-3994.
MSC (2000): Primary 53A10; Secondary 49Q05, 49Q10, 53C42
Posted: January 23, 2004
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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 $\mathbb{R} ^3$.


References:

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D. Hoffman, W. H. Meeks III, The strong halfspace theorem for minimal surfaces. Invent. Math. 101 (1990), no. 2, 373-377. MR 92e:53010

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F. J. López, F. Martín, and S. Morales, Adding handles to Nadirashvili's surfaces. J. Differential Geom. 60 (2002), no. 1, 155-175. MR 2003f:53013

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F. Martín and S. Morales, A complete bounded minimal cylinder in $\mathbb{R} ^3$. Michigan. Math. J. 47 (2000), 499-514. MR 2001m:53015

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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.

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N. Nadirashvili, Hadamard's and Calabi-Yau's conjectures on negatively curved and minimal surfaces. Invent. Math. 126 (1996), 457-465. MR 98d:53014

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R. Osserman, A survey of minimal surfaces. Dover, New York, 1986. MR 87j:53012

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F. Xavier, Convex hulls of complete minimal surfaces. Math. Ann. 269 (1984), no. 2, 179-182. MR 86c:53006

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Additional Information:

Francisco Martín
Affiliation: Departamento de Geometría y Topología, Universidad de Granada, 18071 Granada, Spain
Email: fmartin@ugr.es

Santiago Morales
Affiliation: Departamento de Geometría y Topología, Universidad de Granada, 18071 Granada, Spain
Email: santimo@ugr.es

DOI: 10.1090/S0002-9947-04-03451-8
PII: S 0002-9947(04)03451-8
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
Posted: January 23, 2004
Additional Notes: This research was partially supported by MCYT-FEDER Grant no. BFM2001-3489
Copyright of article: Copyright 2004, American Mathematical Society


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