3 problems

Let $\Gamma$ be a finitely generated subgroup of $\operatorname{Mob}(\mathbb S^n)$ such that its limit set $\Lambda(\Gamma)$ has Hausdorff dimension less than $2$. Small-limit-set…

Let $\Gamma<\operatorname{PU}(n,1)$ with $n\ge 2$, and set $M=M_\Gamma$. For $\epsilon>0$, let $M_{[\epsilon,\infty)}$ denote the thick part of $M$, and suppose it has a convex end…

Let $n\geq 2$, let $\Gamma$ be a group, and let $j,\rho:\Gamma\to\operatorname{SO}_0(n,1)$ be representations such that $j\times\rho(\Gamma)$ acts properly discontinuously and coco…