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Two necessary and sufficient conditions for Möbius subgroups to be g-discontinuous

Published online by Cambridge University Press:  17 April 2009

Zheng-Wu Long
Affiliation:
Institute of Mathematics, Chinese Academy of Sciences, Beijing 100080, Peoples Republic of China, e-mail: [email protected]
Xian-Tao Wang
Affiliation:
Department of Mathematics, Hunan Normal University, Changsha, Hunan 410081, Peoples Republic of China e-mail: [email protected]
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In this paper, two necessary and sufficient conditions of Möbius subgroups to be g-discontinuous are obtained. These are generalisations of Lehner's and Larcher's corresponding results.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Beardon, A.F., The geometry of discrete groups, Graduate Texts in Mathematics 91 (Springer-Verlag, Berlin, Heidelberg, New York, 1983).Google Scholar
[2]Larcher, H., ‘A necessary and sufficient condition for a discrete group of linear fractional transformatins to be discontinuous’, Duke Math. J. 30 (1963), 433436.CrossRefGoogle Scholar
[3]Lehner, J., Discontinuous groups and automorphic functions, Mathematical Surveys VIII (American Mathematical Society, Providence R.I., 1964).Google Scholar
[4]Maskit, B., Kleinian groups (Springer-Verlag, Berlin, Heidelberg, New York, 1988).Google Scholar
[5]Schiff, J. L., Normal families (Springer-Verlag, Berlin, Heidelberg, New York, 1993).CrossRefGoogle Scholar
[6]Tukia, P., ‘Differentiability and rigidity of Möbius groups’, Invent. Math. 82 (1985), 557578.CrossRefGoogle Scholar