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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The limit sets of some infinitely generated Schottky groups


Author: Richard Schwartz
Journal: Trans. Amer. Math. Soc. 335 (1993), 865-875
MSC: Primary 57S30; Secondary 22E40
MathSciNet review: 1148045
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Abstract: Let $ P$ be a packing of balls in Euclidean space $ {E^n}$ having the property that the radius of every ball of $ P$ lies in the interval $ [1/k,k]$. If $ G$ is a Schottky group associated to $ P$, then the Hausdorff dimension of the topological limit set of $ G$ is less than a uniform constant $ C(k,n) < n$. In particular, this limit set has zero volume.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1993-1148045-1
PII: S 0002-9947(1993)1148045-1
Article copyright: © Copyright 1993 American Mathematical Society