## Geometry & Topology

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

#### Abstract

We study graphs of constant mean curvature $H>0$ in $M×ℝ$ for $M$ 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 $M$, having prescribed boundary data, possibly infinite.

#### Article information

Source
Geom. Topol., Volume 16, Number 2 (2012), 1171-1203.

Dates
Revised: 5 March 2012
Accepted: 10 April 2012
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513732416

Digital Object Identifier
doi:10.2140/gt.2012.16.1171

Mathematical Reviews number (MathSciNet)
MR2946806

Zentralblatt MATH identifier
1281.53013

#### Citation

Folha, Abigail; Rosenberg, Harold. The Dirichlet Problem for constant mean curvature graphs in $\mathbb{M}\times\mathbb{R}$. Geom. Topol. 16 (2012), no. 2, 1171--1203. doi:10.2140/gt.2012.16.1171. https://projecteuclid.org/euclid.gt/1513732416

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