Hyperbolic complete minimal surfaces with arbitrary topology
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- by F. J. López
- Trans. Amer. Math. Soc. 350 (1998), 1977-1990
- DOI: https://doi.org/10.1090/S0002-9947-98-01932-1
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Abstract:
We show a method to construct orientable minimal surfaces in $\mathbb {R}^3$ 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.References
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Bibliographic Information
- F. J. López
- Affiliation: Departamento de Geometría y Topología, Facultad de Ciencias, Universidad de Granada, 18071 - Granada (Spain)
- Email: fjlopez@goliat.ugr.es
- 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.
- © Copyright 1998 American Mathematical Society
- 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