Divergence-type semigroups in Kleinian groups and Hausdorff dimension

Abstract

Let $\hat{I}“$ be a non-elementary, non-convex-cocompact Kleinian group acting on ${\mathbb{H}}^d$. We show that the Hausdorff dimension of the sublinearly conical Myrberg limit set of $\hat{I}“$ is equal to the critical exponent of $\hat{I}“$. This gives a different proof of a theorem by M. Mj and W. Yang. Along the way, we construct subsemigroups of $\hat{I}“$ of divergence type and develop the Patterson--Sullivan theory.

v2: corrected a misleading explanation in the introduction. 21 pages, no figures. Comments welcome!