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Quasiconformally homogeneous planar domains
Author(s):
Petra
Bonfert-Taylor;
Edward
C.
Taylor
Journal:
Conform. Geom. Dyn.
12
(2008),
188-198.
MSC (2000):
Primary 30C62;
Secondary 30F45
Posted:
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  and its boundary  implies that the pair  is in fact quasiconformally bi-homogeneous. We also give a geometric and topological characterization of the quasiconformal homogeneity of  or  under the assumption that  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:
10.1090/S1088-4173-08-00189-6
PII:
S 1088-4173(08)00189-6
Received by editor(s):
June 19, 2008
Posted:
December 8, 2008
Additional Notes:
Both authors were supported in part by NSF grant DMS 0706754.
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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