A characterization of quasicircles
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- by Donald K. Blevins and Bruce P. Palka PDF
- Proc. Amer. Math. Soc. 50 (1975), 328-331 Request permission
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 $j = 1,2,3$.References
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Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 50 (1975), 328-331
- MSC: Primary 30A60
- DOI: https://doi.org/10.1090/S0002-9939-1975-0430235-9
- MathSciNet review: 0430235