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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Lindelöf's theorem for hyperbolic catenoids


Authors: Pierre Bérard and Ricardo Sa Earp
Journal: Proc. Amer. Math. Soc. 138 (2010), 3657-3669
MSC (2010): Primary 53C42, 53C21, 58C40
Published electronically: June 15, 2010
MathSciNet review: 2661564
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Abstract: In this paper, we study the maximal stable domains on minimal and constant mean curvature $ 1$ catenoids in hyperbolic space. In particular we investigate whether half-vertical catenoids are maximal stable domains (Lindelöf's property). Our motivation comes from Lindelöf's 1870 paper on catenoids in Euclidean space.


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Additional Information

Pierre Bérard
Affiliation: Institut Fourier, Université Joseph Fourier, BP 74, 38402 Saint Martin d’Hères Cedex, France
Email: Pierre.Berard@ujf-grenoble.fr

Ricardo Sa Earp
Affiliation: Departamento de Matemática, Pontifícia Universidade Católica do Rio de Janeiro, Rua Marquês de São Vicente, 225, Rio de Janeiro, RJ 22453-900, Brazil
Email: earp@mat.puc-rio.br

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10492-6
PII: S 0002-9939(2010)10492-6
Received by editor(s): November 2, 2009
Published electronically: June 15, 2010
Communicated by: Chuu-Lian Terng
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.