SU\G(𝔸)/K·U

The Limit Sets of Some Infinitely Generated Schottky Groups

Richard Schwartz

Type: Article

Publication Date: 1993-02-01

Citations: 0

DOI: https://doi.org/10.2307/2154409

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.

Locations

  • CiteSeer X (The Pennsylvania State University) - View - PDF
  • Transactions of the American Mathematical Society - View - PDF

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Works Cited by This (5)

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+ Real Analysis: Modern Techniques and Their Applications 1984 Gerald B. Folland
+ PDF Chat The density at infinity of a discrete group of hyperbolic motions 1979 Dennis Sullivan
+ PDF Chat The laplacian for domains in hyperbolic space and limit sets of Kleinian groups 1985 Ralph S. Phillips
Peter Sarnak
+ PDF Chat On the bass note of a Schottky group 1988 Peter G. Doyle
+ PDF Chat The Geometry of Discrete Groups 1983 Alan F. Beardon