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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Hausdorff dimension of non-conical limit sets
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by Michael Kapovich and Beibei Liu PDF
Trans. Amer. Math. Soc. 373 (2020), 7207-7224 Request permission

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
  • 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.
  • © Copyright 2020 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 373 (2020), 7207-7224
  • MSC (2010): Primary 20F65, 22E40, 53C20, 57N16
  • DOI: https://doi.org/10.1090/tran/8166
  • MathSciNet review: 4155205