The critical exponent, the Hausdorff dimension of the limit set and the convex core entropy of a Kleinian group
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- by Kurt Falk and Katsuhiko Matsuzaki
- Conform. Geom. Dyn. 19 (2015), 159-196
- DOI: https://doi.org/10.1090/ecgd/279
- Published electronically: June 1, 2015
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Abstract:
In this paper we study the relationship between three numerical invariants associated to a Kleinian group, namely the critical exponent, the Hausdorff dimension of the limit set and the convex core entropy, which coincides with the upper box-counting dimension of the limit set. The Hausdorff dimension of the limit set is naturally bounded below by the critical exponent and above by the convex core entropy. We investigate when these inequalities become strict and when they are equalities.References
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Bibliographic Information
- Kurt Falk
- Affiliation: Universität Bremen, FB 3 - Mathematik, Bibliothekstraße 1, 28359 Bremen, Germany
- MR Author ID: 730899
- Email: khf@math.uni-bremen.de
- Katsuhiko Matsuzaki
- Affiliation: Department of Mathematics, School of Education, Waseda University, Nishi-Waseda 1-6-1, Shinjuku, Tokyo 169-8050, Japan
- MR Author ID: 294335
- ORCID: 0000-0003-0025-5372
- Email: matsuzak@waseda.jp
- Received by editor(s): May 9, 2014
- Published electronically: June 1, 2015
- Additional Notes: The authors were supported by JSPS Grant-in-Aid for Scientific Research (B) #20340030
- © Copyright 2015 American Mathematical Society
- Journal: Conform. Geom. Dyn. 19 (2015), 159-196
- MSC (2000): Primary 30F40; Secondary 37F30
- DOI: https://doi.org/10.1090/ecgd/279
- MathSciNet review: 3351952