Volume 1 (1998)

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ISSN (electronic): 1464-8997
ISSN (print): 1464-8989
On the continuity of bending

Christos Kourouniotis

Geometry & Topology Monographs 1 (1998) 317–334
DOI: 10.2140/gtm.1998.1.317

arXiv: math.GT/9810195

Abstract
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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.

Keywords
Kleinian groups, quasi-Fuchsian groups, geodesic laminations
Mathematical Subject Classification
Primary: 30F40
Secondary: 32G15
References
Publication
Received: 15 November 1997
Published: 26 October 1998
Authors
Christos Kourouniotis
Department of Mathematics
University of Crete
Iraklio
Crete
Greece