Rigidity of Almost-Isometric Universal Covers
Group Theory
2016-07-19 v1 Differential Geometry
Geometric Topology
Abstract
Almost-isometries are quasi-isometries with multiplicative constant one. Lifting a pair of metrics on a compact space gives quasi-isometric metrics on the universal cover. Under some additional hypotheses on the metrics, we show that there is no almost-isometry between the universal covers. We show that Riemannian manifolds which are almost-isometric have the same volume growth entropy. We establish various rigidity results as applications.
Cite
@article{arxiv.1409.3064,
title = {Rigidity of Almost-Isometric Universal Covers},
author = {Aditi Kar and Jean-Francois Lafont and Benjamin Schmidt},
journal= {arXiv preprint arXiv:1409.3064},
year = {2016}
}