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Conditions for Infinitely Generated Kleinian Groups with Small Limit Sets
Andrew Lazowskilazowskia@sacredheart.eduDepartment of Mathematics5151 Park AvenueSacred Heart UniversityFairfield, CT, 06825, USAView full profile →
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- Received:
- 27 Sep 2013
- Accepted:
- 01 Oct 2013
- Published Online:
- 04 Dec 2013
- Article type:
- Article
- Language:
- EN
- Article no.:
- 1726037X.2013.853513
- Pages:
- 87–97
Abstract
We provide conditions for an infinitely generated Kleinian group to have its exponent of convergence arbitrarily small and the Hausdorff dimension of the limit set less than two. We use theory developed by Patterson to show that the exponent of convergence is small. To obtain the conclusion about the Hausdorff dimension of the limit set of the group we use porosity.
Keywords
Subject Classifications
: 30F4037F35
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