Entropy of embedded surfaces in quasi-Fuchsian manifolds

Olivier Glorieux

Vol. 294 (2018), No. 2, 375–400

DOI: 10.2140/pjm.2018.294.375

Abstract

We compare critical exponents for quasi-Fuchsian groups acting on the hyperbolic 3-space and entropy of invariant disks embedded in ${ℍ}^3$. 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