Constant mean curvature graphs on exterior domains of the hyperbolic plane

Abstract

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.

arXiv comment32 pages, 5 figures