REMARKS ON HAUSDORFF DIMENSIONS FOR TRANSIENT LIMIT SETS OF KLEINIAN GROUPS

DOI 2 Citations 28 References

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In this paper we study normal subgroups of Kleinian groups as well as discrepancy groups (d-groups), that are Kleinian groups for which the exponent of convergence is strictly less than the Hausdorff dimension of the limit set. We show that the limit set of a d-group always contains a range of fractal subsets, each containing the set of radial limit points and having Hausdorff dimension strictly less than the Hausdorff dimension of the whole limit set. We then consider normal subgroups $G$ of an arbitrary non-elementary Kleinian group $H$, and show that the exponent of convergence of $G$ is bounded from below by half of the exponent of convergene of $H$. Finally, we give a discussion of various examples of d-groups.

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Details 詳細情報について

  • CRID
    1390282680092720768
  • NII Article ID
    110001043910
  • NII Book ID
    AA00863953
  • DOI
    10.2748/tmj/1113246751
  • ISSN
    2186585X
    00408735
  • MRID
    2097162
  • Text Lang
    en
  • Data Source
    • JaLC
    • Crossref
    • CiNii Articles
  • Abstract License Flag
    Disallowed

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