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arXiv · 1409.3064

Rigidity of Almost-Isometric Universal Covers

Aditi Kar·Jean-Francois Lafont·Benjamin Schmidt
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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.

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Aditi Kar, Jean-Francois Lafont, Benjamin Schmidt. 2014-09-10. Rigidity of Almost-Isometric Universal Covers. https://arxiv.org/abs/1409.3064

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