Kamiya, S. and Parker, J. R. (2008) 'Discrete subgroups of PU(2,1) with screw parabolic elements.', Mathematical proceedings of the Cambridge Philosophical Society., 144 (2). pp. 443-455.
We give a version of Shimizu's lemma for groups of complex hyperbolic isometries one of whose generators is a parabolic screw motion. Suppose that G is a discrete group containing a parabolic screw motion A and let B be any element of G not fixing the fixed point of A. Our result gives a bound on the radius of the isometric spheres of B and B−1 in terms of the translation lengths of A at their centres. We use this result to give a sub-horospherical region precisely invariant under the stabiliser of the fixed point of A in G.
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|Publisher Web site:||http://dx.doi.org/10.1017/S0305004107000941|
|Record Created:||06 Nov 2009 11:50|
|Last Modified:||29 Nov 2011 13:18|
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