A Lower Bound for the Exponent of Convergence of Normal Subgroups of Kleinian Groups

Abstract

We give a short new proof that for each non-elementary Kleinian group $\Gamma$, the exponent of convergence of an arbitrary non-trivial normal subgroup is bounded below by half of the exponent of convergence of $\Gamma$, and that strict inequality holds if $\Gamma$ is of divergence type.

References in corpus (4)

• An extension of Kesten's criterion for amenability to topological Markov chains
• Recurrence and pressure for group extensions
• The critical exponent, the Hausdorff dimension of the limit set and the convex core entropy of a Kleinian group
• Fractal Models for Normal Subgroups of Schottky Groups

Cited by in corpus (2)

• Fractal Models for Normal Subgroups of Schottky Groups
• Conformal Fractals for Normal Subgroups of Free Groups