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Sibirskii Matematicheskii Zhurnal, 2017, Volume 58, Number 3, Pages 485–496
DOI: https://doi.org/10.17377/smzh.2017.58.301 (Mi smj2874) 		 
Quasiconformal extension of quasimöbius mappings of Jordan domains

V. V. Aseev

Sobolev Institute of Mathematics, Novosibirsk, Russia
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DOI: https://doi.org/10.17377/smzh.2017.58.301
Abstract: We introduce the new class of Jordan arcs (curves) of bounded rotation which includes all arcs (curves) of bounded turning. We prove that if the boundary of a Jordan domain has bounded rotation everywhere but possibly one singular point then every quasimöbius embedding of this domain extends to a quasiconformal automorphism of the entire plane.
Keywords: quasiconformal mapping, quasisymmetric mapping, quasimöbius mapping, curve of bounded rotation, curve of bounded turning, quasiconformal extension, Rickman criterion.
Received: 11.08.2016
English version:
Siberian Mathematical Journal, 2017, Volume 58, Issue 3, Pages 373–381
DOI: https://doi.org/10.1134/S0037446617030016
Bibliographic databases:
Document Type: Article
UDC: 517.54
MSC: 35R30
Language: Russian
Citation: V. V. Aseev, “Quasiconformal extension of quasimöbius mappings of Jordan domains”, Sibirsk. Mat. Zh., 58:3 (2017), 485–496; Siberian Math. J., 58:3 (2017), 373–381
Citation in format AMSBIB
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    		Сибирский математический журнал Siberian Mathematical Journal
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