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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Hyperbolic complete minimal surfaces
with arbitrary topology


Author: F. J. López
Journal: Trans. Amer. Math. Soc. 350 (1998), 1977-1990
MSC (1991): Primary 53A10; Secondary 53C42
DOI: https://doi.org/10.1090/S0002-9947-98-01932-1
MathSciNet review: 1422904
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Abstract: We show a method to construct orientable minimal surfaces in $\Bbb R^3$ with arbitrary topology. This procedure gives complete examples of two different kinds: surfaces whose Gauss map omits four points of the sphere and surfaces with a bounded coordinate function. We also apply these ideas to construct stable minimal surfaces with high topology which are incomplete or complete with boundary.


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Additional Information

F. J. López
Affiliation: Departamento de Geometría y Topología, Facultad de Ciencias, Universidad de Granada, 18071 - Granada (Spain)
Email: fjlopez@goliat.ugr.es

DOI: https://doi.org/10.1090/S0002-9947-98-01932-1
Keywords: Minimal surfaces. Riemann surfaces.
Received by editor(s): May 20, 1996
Received by editor(s) in revised form: August 12, 1996
Additional Notes: Research partially supported by DGICYT Grant No. PB94-0796.
Article copyright: © Copyright 1998 American Mathematical Society