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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Bounded turning circles are weak-quasicircles


Author: Daniel Meyer
Journal: Proc. Amer. Math. Soc. 139 (2011), 1751-1761
MSC (2010): Primary 30C65; Secondary 51F99
Published electronically: October 20, 2010
MathSciNet review: 2763763
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Abstract: We show that a metric Jordan curve $ \Gamma$ is bounded turning if and only if there exists a weak-quasisymmetric homeomorphism $ \varphi\colon \mathsf{S}^1 \to \Gamma$.


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Additional Information

Daniel Meyer
Affiliation: Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, FI-00014 University of Helsinki, Finland
Email: dmeyermail@gmail.com

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10634-2
PII: S 0002-9939(2010)10634-2
Keywords: Quasisymmetry, weak-quasisymmetry, bounded turning, weak-quasicircle.
Received by editor(s): March 30, 2010
Received by editor(s) in revised form: May 22, 2010
Published electronically: October 20, 2010
Additional Notes: The author’s research was supported by the Academy of Finland, projects SA-134757 and SA-118634
Communicated by: Mario Bonk
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.