On quasiconformal invariance of convergence and divergence types for Fuchsian groups
Katsuhiko Matsuzaki
Source: Illinois J. Math. Volume 52, Number 4
(2008), 1249-1258.
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.
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Permanent link to this document: http://projecteuclid.org/euclid.ijm/1258554360
Zentralblatt MATH identifier: 05660656
Mathematical Reviews number (MathSciNet): MR2595765
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