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Quasiconformal extension of quasimöbius mappings of Jordan domains. (English. Russian original) Zbl 1445.30007

Sib. Math. J. 58, No. 3, 373-381 (2017); translation from Sib. Mat. Zh. 58, No. 3, 485-496 (2017).
Summary: 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.

MSC:

30C62 Quasiconformal mappings in the complex plane
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