Entropy of embedded surfaces in quasi-fuchsian manifolds

Abstract

We compare critical exponent for quasi-Fuchsian groups acting on the hyperbolic 3-space, ${\mathbb{H}}^3$, and on invariant disks embedded in ${\mathbb{H}}^3$. 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.

arXiv commentAdding a length spectrum rigidity result