Quasiconformally homogeneous planar domains

Bonfert-Taylor, Petra; Taylor, Edward

doi:10.1090/S1088-4173-08-00189-6

Quasiconformally homogeneous planar domains
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by Petra Bonfert-Taylor and Edward C. Taylor

Conform. Geom. Dyn. 12 (2008), 188-198

DOI: https://doi.org/10.1090/S1088-4173-08-00189-6

Published electronically: December 8, 2008

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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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