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Transactions of the American Mathematical Society

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Quasiconformal groups, Patterson-Sullivan theory, and local analysis of limit sets


Authors: Petra Bonfert-Taylor and Edward C. Taylor
Journal: Trans. Amer. Math. Soc. 355 (2003), 787-811
MSC (2000): Primary 30C65; Secondary 30F40, 30F45.
DOI: https://doi.org/10.1090/S0002-9947-02-03134-3
Published electronically: October 2, 2002
MathSciNet review: 1932726
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Abstract: We extend the part of Patterson-Sullivan theory to discrete quasiconformal groups that relates the exponent of convergence of the Poincaré series to the Hausdorff dimension of the limit set. In doing so we define new bi-Lipschitz invariants that localize both the exponent of convergence and the Hausdorff dimension. We find these invariants help to expose and explain the discrepancy between the conformal and quasiconformal setting of Patterson-Sullivan theory.


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Additional Information

Petra Bonfert-Taylor
Affiliation: Department of Mathematics, Wesleyan University, Middletown, Connecticut 06459
Email: pbonfert@wesleyan.edu

Edward C. Taylor
Affiliation: Department of Mathematics, Wesleyan University, Middletown, Connecticut 06459
Email: ectaylor@wesleyan.edu

DOI: https://doi.org/10.1090/S0002-9947-02-03134-3
Keywords: Kleinian groups, discrete quasiconformal groups, Patterson-Sullivan measure, exponent of convergence, Hausdorff dimension.
Received by editor(s): September 15, 2000
Received by editor(s) in revised form: May 14, 2002
Published electronically: October 2, 2002
Additional Notes: The first author was supported in part by NSF grant 0070335
The second author was supported in part by an NSF Postdoctoral Fellowship
Article copyright: © Copyright 2002 American Mathematical Society