The Limit Sets of Some Infinitely Generated Schottky Groups

Abstract

Let $P$ be a packing of balls in Euclidean space ${E^n}$ having the property that the radius of every ball of $P$ lies in the interval $[1/k,k]$. If $G$ is a Schottky group associated to $P$, then the Hausdorff dimension of the topological limit set of $G$ is less than a uniform constant $C(k,n) < n$. In particular, this limit set has zero volume.