An existence and uniqueness result for orientation-reversing harmonic   diffeomorphism from $\mathbb{H}_*^n$ to $\mathbb{R}_*^n$
  In this paper, we prove an existence and uniqueness theorem for orientation-reversing harmonic diffeomorphisms from $\mathbb{H}_*^n$ to $\mathbb{R}_*^n$ with rotational symmetry, which is a generalization of the corresponding result for dimension $2$. 
Shi-Zhong Du and Xu-Qian Fan
math.DG