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Conformal Geometry and Dynamics

ISSN 1088-4173

 
 

 

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
MR Author ID: 617474
Email: pbonfert@wesleyan.edu

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

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.