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THE DISCRETENESS OF THE NORMALIZERS OF HIGHER DIMENSIONAL KLEINIAN GROUPS AND THE ISOMORPHISMS BETWEEN KLEINIAN GROUPS INDUCED BY QUASICONFORMAL MAPPINGS

Published online by Cambridge University Press:  27 July 2005

XIANTAO WANG
Affiliation:
Department of Mathematics, Hunan Normal University, Changsha, Hunan 410081, The People's Republic of China e-mail: xtwang@hunnu.edu.cn
YONGQUN LI
Affiliation:
Department of Mathematics, Hunan Normal University, Changsha, Hunan 410081, The People's Republic of China e-mail: xtwang@hunnu.edu.cn
MAOHUI XIA
Affiliation:
College of Science, Yanshan University, Qinghuangdao, Heibei 066004, The People's Republic of China
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Abstract

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In this paper, we get a necessary and sufficient condition for the normalizers of higher dimensional Kleinian groups to be discrete. Also we obtain a necessary and sufficient condition for the isomorphisms between two higher dimensional Kleinian groups induced by quasiconformal mappings to be the same.

Keywords

Type
Research Article
Copyright
2005 Glasgow Mathematical Journal Trust

Footnotes

The research was partly supported by the Program for NCET in University, NSFs of China and Zhejiang Province and the Foundation for Scholars back from Foreign Countries.