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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We construct an explicit example of a geometrically finite Kleinian group with invariant component
in the Riemann sphere
such that any quasiconformal map from
to the boundary of the convex hull of
in
which extends to the identity map on their common boundary in
, and which is equivariant under the group of Möbius transformations preserving
, must have maximal dilatation
.
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Additional 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
DOI:
https://doi.org/10.1090/S1088-4173-06-00153-6
Received by editor(s):
April 20, 2006
Published electronically:
August 24, 2006
Article copyright:
© Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.