## An explicit counterexample to the equivariant $K=2$ conjecture

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- by Yohei Komori and Charles A. Matthews
- Conform. Geom. Dyn.
**10**(2006), 184-196 - DOI: https://doi.org/10.1090/S1088-4173-06-00153-6
- Published electronically: August 24, 2006
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## Abstract:

We construct an explicit example of a geometrically finite Kleinian group $G$ with invariant component $\Omega$ in the Riemann sphere $\textbf {\hat {C}}$ such that any quasiconformal map from $\Omega$ to the boundary of the convex hull of $\textbf {\hat {C}} - \Omega$ in $\textbf {H^3}$ which extends to the identity map on their common boundary in $\textbf {\hat {C}}$, and which is equivariant under the group of Möbius transformations preserving $\Omega$, must have maximal dilatation $K > 2.002$.## References

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## Bibliographic Information

**Yohei Komori**- Affiliation: Department of Mathematics, Osaka City University, Osaka 558-8585, Japan
- Email: komori@sci.osaka-cu.ac.jp
**Charles A. Matthews**- Affiliation: Department of Mathematics, Southeastern Oklahoma State University, Durant, Oklahoma 74701
- Email: cmatthews@sosu.edu
- Received by editor(s): April 20, 2006
- Published electronically: August 24, 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), 184-196 - MSC (2000): Primary 30F40, 30F60, 32G15, 57M50
- DOI: https://doi.org/10.1090/S1088-4173-06-00153-6
- MathSciNet review: 2261047