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

 

Asymptotically symmetric embeddings and symmetric quasicircles


Authors: Abdelkrim Brania and Shanshuang Yang
Journal: Proc. Amer. Math. Soc. 132 (2004), 2671-2678
MSC (2000): Primary 30C62
Published electronically: March 25, 2004
MathSciNet review: 2054793
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Abstract: A well-known characterization of quasicircles is the following: A Jordan curve $J$ in the complex plane is a quasicircle if and only if it is the image of the unit circle under a quasisymmetric embedding. In this paper we try to characterize a subclass of quasicircles, namely, symmetric quasicircles, by introducing the concept of asymptotically symmetric embeddings. We show that a Jordan curve $J$ in the complex plane is a symmetric quasicircle if and only if it is the image of the unit circle under an asymptotically symmetric embedding.


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Additional Information

Abdelkrim Brania
Affiliation: Department of Mathematics, Morehouse College, Atlanta, Georgia 30314
Email: abrania@morehouse.edu

Shanshuang Yang
Affiliation: Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia 30322
Email: syang@mathcs.emory.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07375-7
PII: S 0002-9939(04)07375-7
Keywords: Quasisymmetric maps, quasicircles, asymptotically symmetric maps, symmetric quasicircles
Received by editor(s): September 18, 2002
Received by editor(s) in revised form: June 12, 2003
Published electronically: March 25, 2004
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2004 American Mathematical Society