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On the asymptotic behavior of a complete bounded minimal surface in
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:
In this paper we construct an example of a complete minimal disk which is properly immersed in a ball of .
References:
-
- 1.
- D. Hoffman, W. H. Meeks III, The strong halfspace theorem for minimal surfaces. Invent. Math. 101 (1990), no. 2, 373-377. MR 92e:53010
- 2.
- 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
- 3.
- F. Martín and S. Morales, A complete bounded minimal cylinder in
. Michigan. Math. J. 47 (2000), 499-514. MR 2001m:53015 - 4.
- S. Morales, On the existence of a proper minimal surface in
with the conformal type of a disk. G.A.F.A., to appear. - 5.
- N. Nadirashvili, Hadamard's and Calabi-Yau's conjectures on negatively curved and minimal surfaces. Invent. Math. 126 (1996), 457-465. MR 98d:53014
- 6.
- R. Osserman, A survey of minimal surfaces. Dover, New York, 1986. MR 87j:53012
- 7.
- 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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