Geometry & Topology Monographs 1 (1998),
The Epstein Birthday Schrift,
paper no. 15, pages 317-334.
On the continuity of bending
We examine the dependence of the deformation obtained by bending
quasi-Fuchsian structures on the bending lamination. We show that when
we consider bending quasi-Fuchsian structures on a closed surface, the
conditions obtained by Epstein and Marden to relate weak convergence
of arbitrary laminations to the convergence of bending cocycles are
not necessary. Bending may not be continuous on the set of all
measured laminations. However we show that if we restrict our
attention to laminations with non negative real and imaginary parts
then the deformation depends continuously on the lamination.
Kleinian groups, quasi-Fuchsian groups, geodesic laminations
AMS subject classification.
Primary: 30F40. Secondary: 32G15.
Submitted: 15 November 1997.
Published: 27 October 1998.
Notes on file formats
Department of Mathematics
University of Crete
Iraklio, Crete, Greece
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