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Conformal Geometry and Dynamics

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Quasiconformally homogeneous planar domains


Authors: Petra Bonfert-Taylor and Edward C. Taylor
Journal: Conform. Geom. Dyn. 12 (2008), 188-198
MSC (2000): Primary 30C62; Secondary 30F45
DOI: https://doi.org/10.1090/S1088-4173-08-00189-6
Published electronically: December 8, 2008
MathSciNet review: 2461511
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Abstract: In this paper we explore the ambient quasiconformal homogeneity of planar domains and their boundaries. We show that the quasiconformal homogeneity of a domain $ D$ and its boundary $ E$ implies that the pair $ (D,E)$ is in fact quasiconformally bi-homogeneous. We also give a geometric and topological characterization of the quasiconformal homogeneity of $ D$ or $ E$ under the assumption that $ E$ is a Cantor set captured by a quasicircle. A collection of examples is provided to demonstrate that certain assumptions are the weakest possible.


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Additional Information

Petra Bonfert-Taylor
Affiliation: Department of Mathematics, Wesleyan University, Middletown, Connecticut 06459
Email: pbonfert@wesleyan.edu

Edward C. Taylor
Affiliation: Department of Mathematics, Wesleyan University, Middletown, Connecticut 06459
Email: ectaylor@wesleyan.edu

DOI: https://doi.org/10.1090/S1088-4173-08-00189-6
Received by editor(s): June 19, 2008
Published electronically: December 8, 2008
Additional Notes: Both authors were supported in part by NSF grant DMS 0706754.
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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