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

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- by Irene Scorza
- Conform. Geom. Dyn.
**10**(2006), 288-325 - DOI: https://doi.org/10.1090/S1088-4173-06-00134-2
- Published electronically: October 10, 2006
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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 $n$.## References

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## Bibliographic Information

**Irene Scorza**- Affiliation: Dipartimento di Matematica, Università di Genova, Via Dodecaneso, 35 - 16146 Genova, Italy
- Email: scorza@dima.unige.it
- Received by editor(s): January 19, 2005
- Published electronically: October 10, 2006
- © Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Conform. Geom. Dyn.
**10**(2006), 288-325 - MSC (2000): Primary 30F40; Secondary 57M50
- DOI: https://doi.org/10.1090/S1088-4173-06-00134-2
- MathSciNet review: 2261053