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A quasiconformal analog of Carathéodory’s criterion for the Möbius property of mappings

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Abstract

In 1937, Carathéodory proved that every injective mapping f: G → f(G) ⊂ \(\bar C\) of a domain G ⊂ \(\bar C\), taking circles to circles, is Möbius. The present article shows that if each injective mapping takes circles onto k-quasicircles then it is K-quasiconformal with \(K \leqslant k + \sqrt {k^2 - 1} \).

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    V. V. Aseev

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  1. V. V. Aseev
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Correspondence to V. V. Aseev.

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Original Russian Text Copyright © 2014 Aseev V.V.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 55, No. 1, pp. 3–10, January–February, 2014.

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Aseev, V.V. A quasiconformal analog of Carathéodory’s criterion for the Möbius property of mappings. Sib Math J 55, 1–6 (2014). https://doi.org/10.1134/S0037446614010017

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  • DOI: https://doi.org/10.1134/S0037446614010017

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