Dirichlet problem at infinity for harmonic maps: rank one symmetric spaces

Abstract:

Given a symmetric space M, of rank one and noncompact type, one compactifies M by adding a sphere at infinity, to obtain a manifold $M\prime$ with boundary. If $\bar M$ is another rank one symmetric space, suppose that $f:\partial M\prime \to \partial \bar M\prime$ is a continuous map. The Dirichlet problem at infinity is to construct a proper harmonic map $u:M \to \bar M$ with boundary values f. This paper concerns existence, uniqueness, and boundary regularity for this Dirichlet problem.