TY - JOUR
T1 - On quasiconformal invariance of convergence and divergence types for Fuchsian groups
AU - Matsuzaki, Katsuhiko
N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2008
Y1 - 2008
N2 - 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.
AB - 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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U2 - 10.1215/ijm/1258554360
DO - 10.1215/ijm/1258554360
M3 - Article
AN - SCOPUS:77955253948
VL - 52
SP - 1249
EP - 1258
JO - Illinois Journal of Mathematics
JF - Illinois Journal of Mathematics
SN - 0019-2082
IS - 4
ER -