Entropy, Critical Exponent and Immersed Surfaces in Hyperbolic 3-Manifolds

Lien-Yung Kao

We consider a ${\pi }_1$--injective immersion $f:\Sigma \to M$ from a compact surface $\Sigma$ to a hyperbolic 3--manifold $M$. Let $\Gamma$ denote the copy of ${\pi }_1\Sigma$ in $\mathrm{Isom}({\mathbb{H}}…