Geometry & Topology Monographs 1 (1998), The Epstein Birthday Schrift, paper no. 15, pages 317-334.

On the continuity of bending

Christos Kourouniotis

Abstract. 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

AMS subject classification. Primary: 30F40. Secondary: 32G15.

E-print: arXiv:math.GT/9810195

Submitted: 15 November 1997. Published: 27 October 1998.

Notes on file formats

Christos Kourouniotis
Department of Mathematics
University of Crete
Iraklio, Crete, Greece

GT home page

EMIS/ELibM Electronic Journals

Outdated Archival Version

These pages are not updated anymore. They reflect the state of 21 Apr 2006. For the current production of this journal, please refer to