Mathematische Zeitschrift

, Volume 272, Issue 1–2, pp 531–550 | Cite as

Constant mean curvature graphs on exterior domains of the hyperbolic plane

Article

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 \({h \in \big(0, \frac{1}{2} \big)}\). We use Schauder theory and a continuity method for solutions of the prescribed mean curvature equation on 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.

Keywords

Constant mean curvature ends Quasi-linear elliptic PDE Exterior domain Non-convex \({\mathbb{H}^2 \times \mathbb{R}}\) 

Mathematics Subject Classification (2000)

35J93 53A10 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversita di BolognaBolognaItaly

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