English

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}
}