Quasiisometric harmonic maps between rank one symmetric spaces

TL;DR

This paper proves that quasiisometric maps between rank one symmetric spaces are close to a unique harmonic map, resolving a significant conjecture in the field.

Contribution

It establishes the uniqueness and existence of harmonic maps near quasiisometric maps, completing the proof of the Schoen-Li-Wang conjecture.

Findings

Quasiisometric maps are within bounded distance from harmonic maps.

The proof confirms the Schoen-Li-Wang conjecture.

Uniqueness of harmonic maps in this context is established.

Abstract

We prove that a quasiisometric 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.