Checking atomicity of conformal ending measures for kleinian groups

Kurt Falk, Katsuhiko Matsuzaki, Bernd O. Stratmann

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    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 nontrivial examples for purely atomic as well as for non-atomic conformal ending measures.

    Original languageEnglish
    Pages (from-to)116-150
    Number of pages35
    JournalConformal Geometry and Dynamics
    Volume3
    Issue number8
    DOIs
    Publication statusPublished - 2010 Jun 30

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    ASJC Scopus subject areas

    • Geometry and Topology

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