Transactions of the American Mathematical Society

Author(s): F. J. López; Francisco Martin; Santiago Morales
Journal: Trans. Amer. Math. Soc. 358 (2006), 3807-3820.
MSC (2000): Primary 53A10; Secondary 49Q05, 49Q10, 53C42
Posted: March 24, 2006
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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.

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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 53A10, 49Q05, 49Q10, 53C42

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

DOI: 10.1090/S0002-9947-06-04004-9
PII: S 0002-9947(06)04004-9
Keywords: Complete bounded minimal surfaces, nonorientable minimal immersions
Received by editor(s): May 24, 2004
Posted: March 24, 2006
Additional Notes: This research was partially supported by MEC-FEDER Grant No. MTM2004-00160
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

Meeks, William H., III(1-MA); Pérez, Joaquín(E-GRAN-G) , Conformal properties in classical minimal surface theory, Surveys in differential geometry. Vol. IX,, International Press, Somerville, 2004, pp. 275--335. MR MR2195411

Colding, Tobias H.; Minicozzi, William P., II, Minimal submanifolds, Bull. London Math. Soc. 38 (2006), 353--395. (English) MR 2239032

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