Quasiconformal extension of quasimöbius mappings of Jordan domains
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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.
Keywordsquasiconformal mapping quasisymmetric mapping quasimöbius mapping curve of bounded rotation curve of bounded turning quasiconformal extension Rickman criterion
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