#### 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 ${ℍ}^{3}$. 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