V. V. Aseev, “The quasimöbius property on small circles and quasiconformality”, Sibirsk. Mat. Zh., 2013, Volume 54, Number 2,Pages <nobr>258

This article is cited in 5 papers

The quasimöbius property on small circles and quasiconformality

V. V. Aseev

Sobolev Institute of Mathematics, Novosibirsk, Russia

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

Keywords: quasimöbius embedding, quasisymmetric embedding, distortion function, quasiconformal mapping, quasiconformality coefficient, Möbius midpoint condition, absolute cross-ratio, anharmonic ratio, chordal metric.

UDC: 517.54

Received: 11.11.2011