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ArticleOriginal scientific text

Title

The box-counting dimension for geometrically finite Kleinian groups

Authors 1, 2

Affiliations

  1. Mathematisches Institut der Universität Göttingen, SFB 170 Bunsenstr. 3-5, 3400 Göttingen, Germany
  2. Department of Mathematics, University of North Texas, Denton, Texas 76203-5116, U.S.A.

Abstract

We calculate the box-counting dimension of the limit set of a general geometrically finite Kleinian group. Using the 'global measure formula' for the Patterson measure and using an estimate on the horoball counting function we show that the Hausdorff dimension of the limit set is equal to both: the box-counting dimension and packing dimension of the limit set. Thus, by a result of Sullivan, we conclude that for a geometrically finite group these three different types of dimension coincide with the exponent of convergence of the group.

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Additional information

http://matwbn.icm.edu.pl/ksiazki/fm/fm149/fm14916.pdf

Fundamenta Mathematicae
1996/149/1
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Pages:
83-93
Main language of publication
English
Received
1995-05-21
Accepted
1995-08-07
Published
1996
Exact and natural sciences