We prove that a quasi-isometric map between rank one symmetric spaces is within bounded distance from a unique harmonic map. In particular, this completes the proof of the Schoen-Li-Wang conjecture.
Yves Benoist. Dominique Hulin. "Harmonic quasi-isometric maps between rank one symmetric spaces." Ann. of Math. (2) 185 (3) 895 - 917, May 2017. https://doi.org/10.4007/annals.2017.185.3.4