The small-limit-set geometric finiteness conjecture

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 geometric finiteness conjecture. The group $\Gamma$ is geometrically finite. The conjecture is known for $n=2$ by Bishop and Jones, and a conformally finite higher-dimensional case is stated as a theorem; the general case remains open in the source.