Growth and cogrowth tightness of Kleinian and hyperbolic groups (Geometry and Analysis of Discrete Groups and Hyperbolic Spaces)

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Description

Let G be a non-elementary discrete isometry group of the hyperbolic space or more generally a proper geodesic Gromov hyperbolic space X. We say that G is growth tight if for any non-trivial normal subgroup H the critical exponent k(H＼G) of the quotient group is strictly smaller than k(G). Moreover, G is cogrowth tight if the critical exponent δ(H) of any such H is strictly greater than δ(G)/2. We review recent results on these properties of G with the addition of certain new observation. In particular, we see that a non-elementary quasi-convex cocompact discrete isometry group G of X is growth tight.

Journal

  • RIMS Kokyuroku Bessatsu

    RIMS Kokyuroku Bessatsu B66 21-36, 2017-06

    Research Institute for Mathematical Sciences, Kyoto University

Keywords

Details 詳細情報について

  • CRID
    1050564288413975424
  • NII Article ID
    120006715416
  • NII Book ID
    AA12196120
  • ISSN
    18816193
  • HANDLE
    2433/243691
  • Text Lang
    en
  • Article Type
    departmental bulletin paper
  • Data Source
    • IRDB
    • CiNii Articles

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