Proper harmonic maps between asymptotically hyperbolic manifolds

Generalizing the result of Li and Tam for the hyperbolic spaces, we prove an existence theorem on the Dirichlet problem for harmonic maps with C1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^1$$\end{document} boundary conditions at infinity between asymptotically hyperbolic manifolds.