Harmonic maps with singular boundary value from complex hyperbolic spaces into rank one symmetric spaces

Abstract

In this paper we consider the Dirichlet problem at infinity of proper harmonic maps from noncompact complex hyperbolic space \(\mathbf{CH^m}\) to a rank one symmetric space N of noncompact type with singular boundary data \(f: \mathbf{S^{2m-1}}\longrightarrow \partial_\infty N\). Under some conditions on f, we show that the Dirichlet problem at infinity admits a harmonic map which assumes the boundary data f continuously.