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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A uniqueness theorem for the singly periodic genus-one helicoid


Authors: Antonio Alarcón, Leonor Ferrer and Francisco Martín
Journal: Trans. Amer. Math. Soc. 359 (2007), 2819-2829
MSC (2000): Primary 53A10; Secondary 53C42
Published electronically: January 26, 2007
MathSciNet review: 2286058
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Abstract: The singly periodic genus-one helicoid was in the origin of the discovery of the first example of a complete minimal surface with finite topology but infinite total curvature, the celebrated Hoffman-Karcher-Wei's genus one helicoid. The objective of this paper is to give a uniqueness theorem for the singly periodic genus-one helicoid provided the existence of one symmetry.


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Additional Information

Antonio Alarcón
Affiliation: Departamento de Geometría y Topología, Universidad de Granada, 18071, Granada, Spain
Email: alarcon@ugr.es

Leonor Ferrer
Affiliation: Departamento de Geometría y Topología, Universidad de Granada, 18071, Granada, Spain
Email: lferrer@ugr.es

Francisco Martín
Affiliation: Departamento de Geometría y Topología, Universidad de Granada, 18071, Granada, Spain
Email: fmartin@ugr.es

DOI: http://dx.doi.org/10.1090/S0002-9947-07-04093-7
PII: S 0002-9947(07)04093-7
Keywords: Properly embedded minimal surfaces, helicoidal ends
Received by editor(s): May 4, 2005
Published electronically: January 26, 2007
Additional Notes: Research for this work was partially supported by MEC-FEDER grant number MTM2004-00160.
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.