On quasiconformal invariance of convergence and divergence types for Fuchsian groups

Research output: Contribution to journalArticle

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
Externally publishedYes

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Fuchsian Group
Quasiconformal
Invariance
Divergence
Riemann Surface
Automorphism
Critical Exponents
Unit Disk
Quotient
Subgroup
Invariant
Series

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On quasiconformal invariance of convergence and divergence types for Fuchsian groups. / Matsuzaki, Katsuhiko.

In: Illinois Journal of Mathematics, Vol. 52, No. 4, 2008, p. 1249-1258.

Research output: Contribution to journalArticle

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