Large and small covers of a hyperbolic manifold

Petra Bonfert-Taylor, Katsuhiko Matsuzaki*, Edward C. Taylor

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


The exponent of convergence of a non-elementary discrete group of hyperbolic isometries measures the Hausdorff dimension of the conical limit set. In passing to a non-trivial regular cover the resulting limit sets are point-wise equal though the exponent of convergence of the cover uniformization may be strictly less than the exponent of convergence of the base. We show in this paper that, for closed hyperbolic surfaces, the previously established lower bound of one half on the exponent of convergence of "small" regular covers is sharp but is not attained. We also consider "large" (non-regular) covers. Here large and small are descriptive of the size of the exponent of convergence.We show that a Kleinian group that uniformizes a manifold homeomorphic to a surface fibering over a circle contains a Schottky subgroup whose exponent of convergence is arbitrarily close to two.

Original languageEnglish
Pages (from-to)455-470
Number of pages16
JournalJournal of Geometric Analysis
Issue number2
Publication statusPublished - 2012 Apr
Externally publishedYes


  • Bottom of spectrum
  • Conical limit set
  • Exponent of convergence
  • Geodesic flow
  • Kleinian groups

ASJC Scopus subject areas

  • Geometry and Topology


Dive into the research topics of 'Large and small covers of a hyperbolic manifold'. Together they form a unique fingerprint.

Cite this