The critical exponent, the hausdorff dimension of the limit set and the convex core entropy of a Kleinian group

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    In this paper we study the relationship between three numerical invariants associated to a Kleinian group, namely the critical exponent, the Hausdorff dimension of the limit set and the convex core entropy, which coincides with the upper box-counting dimension of the limit set. The Hausdorff dimension of the limit set is naturally bounded below by the critical exponent and above by the convex core entropy. We investigate when these inequalities become strict and when they are equalities.

    元の言語English
    ページ(範囲)159-196
    ページ数38
    ジャーナルConformal Geometry and Dynamics
    19
    発行部数8
    DOI
    出版物ステータスPublished - 2015

    ASJC Scopus subject areas

    • Geometry and Topology

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