A Harmonic-Map Proof of Mostow Rigidity
Differential Geometry
2026-07-29 v1
Abstract
Given an isomorphism between the fundamental groups of two compact hyperbolic manifolds of dimension at least three, we consider the associated equivariant harmonic lift. We establish a sharp pointwise gradient estimate for this lift. This yields a harmonic-map proof of Mostow rigidity.
Cite
@article{arxiv.2607.26677,
title = {A Harmonic-Map Proof of Mostow Rigidity},
author = {Guoyi Xu},
journal= {arXiv preprint arXiv:2607.26677},
year = {2026}
}