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