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The
Dirichlet Problem for constant mean curvature graphs in
$\mathbb{M}\times\mathbb{R}$
Abigail Folha and Harold Rosenberg |
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Geometry & Topology 16 (2012) 1171–1203
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Abstract |
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We study graphs of constant mean curvature in for a Hadamard surface, ie a complete simply connected surface with curvature bounded above by a negative constant . We find necessary and sufficient conditions for the existence of these graphs over bounded domains in , having prescribed boundary data, possibly infinite. |
Keywords
Hadamard surface, constant mean curvature, Dirichlet
problem
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Mathematical Subject Classification 2010
Primary: 53A10
Secondary: 53C42
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References |
Publication
Received: 21 February 2011
Revised: 5 March 2012
Accepted: 10 April 2012
Published: 23 June 2012
Proposed: Tobias H Colding
Seconded: John Lott, Yasha Eliashberg
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Authors |
| Abigail Folha | |
| Instituto de Matemática –
Departamento de Geometria Universidade Federal Fluminense R Mário Santos Braga, s/n Campus do Valonguinho CEP 24020-140 Niterói, RJ Brazil |
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| Harold Rosenberg | |
| Instituto de Matemática Pura e
Aplicada Estrada Dona Castorina 110 CEP 22460-320 Rio de Janeiro, RJ Brazil |
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| http://www.math.jussieu.fr/~rosen/ | |
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