Checking atomicity of conformal ending measures for kleinian groups

Kurt Falk, Katsuhiko Matsuzaki, Bernd O. Stratmann

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    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

    Fingerprint

    Conformal Measure
    Atomicity
    Kleinian Groups
    Limit Set
    Fixed point
    Sufficient Conditions
    Arbitrary

    ASJC Scopus subject areas

    • Geometry and Topology

    Cite this

    Checking atomicity of conformal ending measures for kleinian groups. / Falk, Kurt; Matsuzaki, Katsuhiko; Stratmann, Bernd O.

    In: Conformal Geometry and Dynamics, Vol. 3, No. 8, 30.06.2010, p. 116-150.

    Research output: Contribution to journalArticle

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