THE DIRICHLET PROBLEM FOR HARMONIC MAPS BETWEEN DAMEK-RICCI SPACES

Abstract

A Damek-Ricci space has nonpositive curvature. Thus we can consider the Eberlein-O'Neill compactifications adding the sphere at infinity. In this paper, we prove the existence and uniqueness of a solution to the Dirichlet problem at infinity for harmonic maps between Damek-Ricci spaces.