The Dirichlet problem at infinity for harmonic map equations arising from constant mean curvature surfaces in the hyperbolic 3-space

Abstract

The purpose of this paper is to study some uniqueness, existence and regularity properties of the Dirichlet problem at infinity for proper harmonic maps from the hyperbolic m-space to the open unit n-ball with a specific incomplete metric. When m=n=2, harmonic solutions of this Dirichlet problem yield complete constant mean curvature surfaces in the hyperbolic 3-space.