#### Volume 16, issue 2 (2012)

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The Dirichlet Problem for constant mean curvature graphs in $\mathbb{M}\times\mathbb{R}$

### Abigail Folha and Harold Rosenberg

Geometry & Topology 16 (2012) 1171–1203
##### Abstract

We study graphs of constant mean curvature $H>0$ in $\mathbb{M}×ℝ$ for $\mathbb{M}$ a Hadamard surface, ie a complete simply connected surface with curvature bounded above by a negative constant $-a$. We find necessary and sufficient conditions for the existence of these graphs over bounded domains in $\mathbb{M}$, having prescribed boundary data, possibly infinite.

##### Keywords
Hadamard surface, constant mean curvature, Dirichlet problem
Primary: 53A10
Secondary: 53C42
##### 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
##### 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 Harold Rosenberg Instituto de Matemática Pura e Aplicada Estrada Dona Castorina 110 CEP 22460-320 Rio de Janeiro, RJ Brazil http://www.math.jussieu.fr/~rosen/