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Conformal Geometry and Dynamics

ISSN 1088-4173



The core chain of circles of Maskit’s embedding for once-punctured torus groups

Author: Irene Scorza
Journal: Conform. Geom. Dyn. 10 (2006), 288-325
MSC (2000): Primary 30F40; Secondary 57M50
Published electronically: October 10, 2006
MathSciNet review: 2261053
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Abstract: In this paper, we describe the limit set $\Lambda _n$ of a sequence of manifolds $N_n$ in the boundary of Maskit’s embedding of the once-punctured torus. We prove that $\Lambda _n$ contains a chain of tangent circles $\{C_{n,j}\}$ that are described from the end invariants of the manifold. In particular, we give estimates in terms of $n$ of the radii $r_{n,j}$ of the circles and prove that $r_{n,j}$ decrease when $n$ tends to infinity. We then apply these results to McShane’s identity, to obtain an estimate of the width of the limit set in terms of $n$.

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Irene Scorza
Affiliation: Dipartimento di Matematica, Università di Genova, Via Dodecaneso, 35 - 16146 Genova, Italy

Keywords: Kleinian groups, limit sets.
Received by editor(s): January 19, 2005
Published electronically: October 10, 2006
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.