On the continuity of bending

Details On the continuity of bending On the continuity of bending

1998-10-27

arxiv.org/abs/math/9810195v1

Geom. Topol. Monogr. 1 (1998), 317-334

Mathematics

Geometric Topology

18 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTMon1/paper15.abs.html

Scientific paper

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.

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