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On Ford isometric spheres in complex hyperbolic space

Published online by Cambridge University Press:  24 October 2008

John R. Parker
John R. Parker
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL
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Abstract

The complex hyperbolic version of Shimizu's lemma gives an upper bound on the radii of isometric spheres of maps in a discrete subgroup of PU(n, 1) containing a vertical Heisenberg translation. The purpose of this paper is to show that in a neighbourhood of this bound radii of isometric spheres only take values in a particular discrete set. When the group contains certain ellipto-parabolic maps this upper bound can be improved and the set of values of the radii is more restricted. Examples are given that show that these results cannot be improved.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 115 , Issue 3 , May 1994 , pp. 501 - 512
Copyright
Copyright © Cambridge Philosophical Society 1994

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