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The quasimöbius property on small circles and quasiconformality

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Abstract

We prove that every mapping, without requiring its injectivity or continuity, of a domain of the extended plane which is ω-quasimöbius on sufficiently small circles is locally quasiconformal in this domain with an upper bound on the quasiconformality coefficient depending only on ω. We obtain a similar result for the η-quasisymmetric mappings on small circles (in the Euclidean and chordal metrics), as well as for the mappings satisfying the local Möbius midpoint condition.

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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 © 2013 Aseev V.V.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 54, No. 2, pp. 258–269, March–April, 2013.

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Aseev, V.V. The quasimöbius property on small circles and quasiconformality. Sib Math J 54, 196–204 (2013). https://doi.org/10.1134/S003744661302002X

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