Sequences of Porous Sets and an Application to Kleinian Groups

被引：0

作者：

Lazowski, Andrew ^{[1
]}

机构：

[1] Sacred Heart Univ, Dept Math, 5151 Pk Ave, Fairfield, CT 06825 USA

来源：

QUAESTIONES MATHEMATICAE | 2022年 / 45卷 / 07期

关键词：

Porosity; Kleinian groups; Hausdorff dimension; DIMENSION;

D O I：

10.2989/16073606.2021.1926369

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：1013 / 1016

页数：4

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