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Transactions of the American Mathematical Society

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Hausdorff dimension of non-conical limit sets


Authors: Michael Kapovich and Beibei Liu
Journal: Trans. Amer. Math. Soc. 373 (2020), 7207-7224
MSC (2010): Primary 20F65, 22E40, 53C20, 57N16.
DOI: https://doi.org/10.1090/tran/8166
Published electronically: August 11, 2020
MathSciNet review: 4155205
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Abstract: Geometrically infinite Kleinian groups have non-conical limit sets with the cardinality of the continuum. In this paper, we construct a geometrically infinite Fuchsian group such that the Hausdorff dimension of the non-conical limit set equals zero. For finitely generated, geometrically infinite Kleinian groups, we prove that the Hausdorff dimension of the non-conical limit set is positive.


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Additional Information

Michael Kapovich
Affiliation: Department of Mathematics, University of California Davis, One Shields Avenue, Davis, California 95616
MR Author ID: 98110
Email: kapovich@math.ucdavis.edu

Beibei Liu
Affiliation: Max Planck Institute of Mathematics, Vivatsgasse 7, 53111 Bonn, Germany
MR Author ID: 1308544
Email: bbliumath@gmail.com

Keywords: Hausdorff dimension, non-conical limit set, geometric infiniteness.
Received by editor(s): October 13, 2019
Received by editor(s) in revised form: February 4, 2020
Published electronically: August 11, 2020
Additional Notes: During the work on this paper the first author was partly supported by the NSF grant DMS-16-04241.
The second author is grateful to Max Planck Institute for Mathematics in Bonn for its hospitality and financial support.
Article copyright: © Copyright 2020 American Mathematical Society