An explicit counterexample to the equivariant 𝐾=2 conjecture

Komori, Yohei; Matthews, Charles

doi:10.1090/S1088-4173-06-00153-6

An explicit counterexample to the equivariant conjecture

Authors: Yohei Komori and Charles A. Matthews
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
Published electronically: August 24, 2006
MathSciNet review: 2261047
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Abstract: We construct an explicit example of a geometrically finite Kleinian group with invariant component $\Omega$ in the Riemann sphere ${\bf\hat{C}}$ such that any quasiconformal map from $\Omega$ to the boundary of the convex hull of ${\bf\hat{C}} - \Omega$ in ${\bf H^3}$ which extends to the identity map on their common boundary in ${\bf\hat{C}}$ , and which is equivariant under the group of Möbius transformations preserving $\Omega$ , must have maximal dilatation .

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