Vol. 294, No. 2, 2018

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Entropy of embedded surfaces in quasi-Fuchsian manifolds

Olivier Glorieux

Vol. 294 (2018), No. 2, 375–400
Abstract

We compare critical exponents for quasi-Fuchsian groups acting on the hyperbolic 3-space and entropy of invariant disks embedded in 3 . We give a rigidity theorem for all embedded surfaces when the action is Fuchsian and a rigidity theorem for negatively curved surfaces when the action is quasi-Fuchsian.

Keywords
hyperbolic geometry, entropy, quasi-Fuchsian, length spectrum
Mathematical Subject Classification 2010
Primary: 32Q45, 51F99, 51K99, 53A35
Milestones
Received: 2 February 2016
Revised: 14 November 2017
Accepted: 14 November 2017
Published: 20 February 2018
Authors
Olivier Glorieux
University of Luxembourg
Esch-sur-Alzette
Luxembourg