On quasiconformal invariance of convergence and divergence types for Fuchsian groups

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Abstract

We characterize convergence and divergence types for Fuchsian groups in terms of the critical exponent of convergence and modified functions of the Poincaré series for certain subgroups associated with ends of the quotient Riemann surfaces. As an application of this result, we prove that convergence and divergence type are not invariant under a quasiconformal automorphism of the unit disk.

Original languageEnglish
Pages (from-to)1249-1258
Number of pages10
JournalIllinois Journal of Mathematics
Volume52
Issue number4
Publication statusPublished - 2008 Dec 1

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ASJC Scopus subject areas

  • Mathematics(all)

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