Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 32, 2007, 179-198

ON THE SHAPE OF BERS-MASKIT SLICES

Yohei Komori and Jouni Parkkonen

Osaka City University, Department of Mathematics
3-3-138, Sugimoto, Sumiyoshi-ku, Osaka, 558-8585 Japan; komori 'at' sci.osaka-cu.ac.jp

University of Jyväskylä, Department of Mathematics and Statistics
P.O. Box 35, 40014 University of Jyväskylä, Finland; parkkone 'at' maths.jyu.fi

Abstract. We consider complex one-dimensional Bers-Maskit slices through the deformation space of quasifuchsian groups which uniformize a pair of punctured tori. In these slices, the pleating locus on one of the components of the convex hull boundary of the quotient three-manifold has constant rational pleating and constant hyperbolic length. We show that the boundary of such a slice is a Jordan curve which is cusped at a countable dense set of points. We will also show that the slices are not vertically convex, proving the phenomenon observed numerically by Epstein, Marden and Markovic.

2000 Mathematics Subject Classification: Primary 30F40, 30F60, 57M50.

Key words: Kleinian groups, punctured torus groups, Teichmüller space, pleating coordinates, end invariants.

Reference to this article: Y. Komori and J. Parkkonen: On the shape of Bers-Maskit slices. Ann. Acad. Sci. Fenn. Math. 32 (2007), 179-198.

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