Harmonic quasi-isometries between negatively curved manifolds
Very recently, Markovic, Lemm-Markovic and Benoist-Hulin, established the existence of a harmonic mapping in the homotopy class of an arbitrary quasi-isometry between rank 1 symmetric spaces. I will discuss these results and the more general conjecture which states that this result holds for quasi-isometries between negatively curved manifolds and metric spaces.
