Harmonic maps with singular boundary value from complex hyperbolic spaces into rank one symmetric spaces (Q1566859)

The authors consider the Dirichlet problem at infinity for proper harmonic maps from the complex hyperbolic space \(CH^m\) to a rank one symmetric space \(N\) of noncompact type with singular boundary data \(f:S^{2m-1}\to \partial_{\infty}N\). Here singular means roughly that the energy density of \(f\) may vanish somewhere, which is the case not covered by \textit{H. Donnelly} [Trans. Am. Math. Soc. 344, No. 2, 713-735 (1994; Zbl 0812.58020)]. Under several conditions on \(f\), it is shown that the Dirichlet problem at infinity admits a harmonic map which assumes the boundary data \(f\) continuously. The main tool in the proof is an explicit formula for the minimal positive Green function of \(CH^m\).