Constant mean curvature graphs on exterior domains of the hyperbolic plane

Details Constant mean curvature graphs on exterior domains of the hyperbolic plane Constant mean curvature graphs on exterior domains of the hyperbolic plane

2011-03-23

arxiv.org/abs/1103.4564v2

Mathematics

Analysis of PDEs

32 pages, 5 figures

Scientific paper

We prove an existence result for non rotational constant mean curvature ends in $\mathbb{H}^2 \times \mathbb{R}$, where $\mathbb{H}^2$ is the hyperbolic real plane. The value of the curvature is $h \, \in \, (0, 1/2)$. We use Schauder theory and a continuity method for solution of the prescribed mean curvature equation of exterior domains of $\mathbb{H}^2$. We also prove a fine property of the asymptotic behavior of the rotational ends introduced by Sa Earp and Toubiana.

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