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

A characterization of quasicircles


Authors: Donald K. Blevins and Bruce P. Palka
Journal: Proc. Amer. Math. Soc. 50 (1975), 328-331
MSC: Primary 30A60
MathSciNet review: 0430235
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Abstract: In this paper the following result is established: a Jordan curve $ \Gamma $ in the extended plane $ {\mathbf{\bar C}}$ is a quasicircle if and only if there is a $ K,1 \leq K < \infty $, such that, given ordered triples $ {z_1},{z_2},{z_3}$ and $ {w_1},{w_2},{w_3}$ of points on $ \Gamma $, there exists a $ K$-quasiconformal mapping $ h$ of $ {\mathbf{\bar C}}$ onto itself with $ h(\Gamma ) = \Gamma $ and $ h({z_j}) = {w_j}$ for $ j = 1,2,3$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0430235-9
PII: S 0002-9939(1975)0430235-9
Keywords: Jordan curve, triple-transitivity, quasiconformal mapping, quasicircle
Article copyright: © Copyright 1975 American Mathematical Society