Abstract

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.

中文翻译：

---

多孔集序列及其在克莱因群中的应用

摘要

在本文中，我们证明了在 Hausdorff 收敛下的一系列多孔集的极限也是多孔的。然后将这个纯粹的拓扑结果应用于克莱因群论，以构造一个收敛指数任意小且极限集的豪斯多夫维数严格小于 2 的克莱因群。