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Conformal Geometry and Dynamics

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

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.5.

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Checking atomicity of conformal ending measures for Kleinian groups
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by Kurt Falk, Katsuhiko Matsuzaki and Bernd O. Stratmann PDF
Conform. Geom. Dyn. 14 (2010), 167-183 Request permission

Abstract:

In this paper we address questions of continuity and atomicity of conformal ending measures for arbitrary non-elementary Kleinian groups. We give sufficient conditions under which such ending measures are purely atomic. Moreover, we will show that if a conformal ending measure has an atom which is contained in the big horospherical limit set, then this atom has to be a parabolic fixed point. Also, we give detailed discussions of non-trivial examples for purely atomic as well as for non-atomic conformal ending measures.
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Additional Information
  • Kurt Falk
  • Affiliation: Fachbereich 3 - Mathematik und Informatik, Universität Bremen, Bibliothekstr. 1, D-28359 Bremen, Germany
  • Email: khf@math.uni-bremen.de
  • Katsuhiko Matsuzaki
  • Affiliation: Department of Mathematics, School of Education, Waseda University, Shinjuku, Tokyo 169-8050, Japan
  • Email: matsuzak@waseda.jp
  • Bernd O. Stratmann
  • Affiliation: Fachbereich 3 - Mathematik und Informatik, Universität Bremen, Bibliothekstr. 1, D-28359 Bremen, Germany
  • Email: bos@math.uni-bremen.de
  • Received by editor(s): March 18, 2009
  • Published electronically: June 30, 2010
  • Additional Notes: The first author was supported by the Science Foundation Ireland
    The second author was supported by JSPS Grant B #20340030
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Conform. Geom. Dyn. 14 (2010), 167-183
  • MSC (2010): Primary 30F40, 37F35; Secondary 37F30, 28A80
  • DOI: https://doi.org/10.1090/S1088-4173-2010-00209-2
  • MathSciNet review: 2660143