Complete nonorientable minimal surfaces in a ball of $\mathbb {R}^3$
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- by F. J. López, Francisco Martin and Santiago Morales PDF
- Trans. Amer. Math. Soc. 358 (2006), 3807-3820 Request permission
Abstract:
The existence of complete minimal surfaces in a ball was proved by N. Nadirashvili in 1996. However, the construction of such surfaces with nontrivial topology remained open. In 2002, the authors showed examples of complete orientable minimal surfaces with arbitrary genus and one end. In this paper we construct complete bounded nonorientable minimal surfaces in $\mathbb {R}^3$ with arbitrary finite topology. The method we present here can also be used to construct orientable complete minimal surfaces with arbitrary genus and number of ends.References
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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@ugr.es
- Francisco Martin
- Affiliation: Departamento de Geometría y Topología, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
- Email: fmartin@ugr.es
- Santiago Morales
- Affiliation: Departamento de Geometría y Topología, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
- Email: santimo@ugr.es
- Received by editor(s): May 24, 2004
- Published electronically: March 24, 2006
- Additional Notes: This research was partially supported by MEC-FEDER Grant No. MTM2004-00160
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 358 (2006), 3807-3820
- MSC (2000): Primary 53A10; Secondary 49Q05, 49Q10, 53C42
- DOI: https://doi.org/10.1090/S0002-9947-06-04004-9
- MathSciNet review: 2219000