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JOURNALS // Sibirskii Matematicheskii Zhurnal // Archive

Sibirsk. Mat. Zh., 2021 Volume 62, Number 5, Pages 965–982 (Mi smj7608)

This article is cited in 2 papers

On the geometric definition of quasiconformality

V. V. Aseev

Sobolev Institute of Mathematics, Novosibirsk, Russia

Abstract: Considering a homeomorphism of the plane onto itself, we prove that the criterion of quasiconformality is the presence of an upper bound for the modulus of the family of curves joining the images of the opposite sides of an arbitrary oriented square with the sides parallel to the coordinate axes.

Keywords: quasiconformal mapping, modulus of a family of curves, oriented square, bounded turning, quasicircle, graph convergence.

UDC: 517.54

MSC: 35R30

Received: 11.01.2021
Revised: 11.01.2021
Accepted: 11.06.2021

DOI: 10.33048/smzh.2021.62.502


 English version:
Siberian Mathematical Journal, 2021, 62:5, 782–795

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© Steklov Math. Inst. of RAS, 2025