Sequences of Porous Sets and an Application to Kleinian Groups

Document Type

Peer-Reviewed Article

Publication Date

2022

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.

Comments

Published online: 15 Jun 2021.

Mathematics Subject Classification (2020): 30F40, 37F35, 54A20

DOI

10.2989/16073606.2021.1926369

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