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

   

 

Existence of vertical ends of mean curvature $ 1/2$ in $ \mathbb{H}^2 \times\mathbb{R}$


Authors: Maria Fernanda Elbert, Barbara Nelli and Ricardo Sa Earp
Journal: Trans. Amer. Math. Soc. 364 (2012), 1179-1191
MSC (2010): Primary 53C42, 35J25
Published electronically: November 7, 2011
MathSciNet review: 2869173
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Abstract: We prove the existence of graphs over exterior domains of $ \mathbb{H}^2\times \{0\},$ of constant mean curvature $ H=\frac {1}{2}$ in $ \mathbb{H}^2\times \mathbb{R}$ and weak growth equal to the embedded rotational examples.


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Maria Fernanda Elbert
Affiliation: Departamento de Métodos Matemáticos, Instituto de Matemática, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, CEP: 21945-970 Rio de Janeiro-RJ, Brazil
Email: fernanda@im.ufrj.br

Barbara Nelli
Affiliation: Dipartimento di Matematica, Universitá di L’Aquila, 67100 L’Aquila, Italia
Email: nelli@univaq.it

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

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05361-4
Received by editor(s): April 8, 2008
Received by editor(s) in revised form: February 21, 2010
Published electronically: November 7, 2011
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.