A Harmonic-Map Proof of Mostow Rigidity
arXiv:2607.26677
summary
The paper proves Mostow rigidity for compact hyperbolic manifolds of dimension ≥3 by establishing a sharp pointwise gradient estimate for an equivariant harmonic lift associated to an isomorphism of fundamental groups.
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.
Topics & keywords
#hyperbolic manifolds#mostow rigidity#harmonic maps#gradient estimates#fundamental groupsequivariant harmonic liftpointwise gradient estimatecompact hyperbolic manifolddimension ≥3isomorphism of fundamental groups