Sequences of Porous Sets and an Application to Kleinian Groups
In this paper we show that the limit of a sequence of porous sets under Hausdorﬀ convergence is also porous. This purely topological result is then applied to Kleinian group theory in order to construct a Kleinian group with exponent of convergence arbitrarily small and Hausdorﬀ dimension of the limit set strictly less than two.
Lazowski, A. (2021). Sequences of porous sets and an application to Kleinian Groups. Quaestiones Mathematicae. Doi: 10.2989/16073606.2021.1926369