A note on V\"ais\"al\"a's problem concerning free quasiconformal mappings
Qingshan Zhou, Yaxiang Li, Antti Rasila
TL;DR
This paper addresses V"ais"al"a's problem by showing that local free quasiconformal mappings become global under certain local symmetry conditions, advancing understanding of their structural properties.
Contribution
It provides partial solutions to V"ais"al"a's problem, establishing conditions under which local free quasiconformal mappings are globally free quasiconformal.
Findings
Local free quasiconformal mappings are globally free quasiconformal under locally relative quasisymmetry.
Partial solutions to V"ais"al"a's problem are presented.
The paper clarifies the conditions linking local and global properties of quasiconformal mappings.
Abstract
In this paper, we provide partial solutions to a problem raised by V\"ais\"al\"a on local properties of free quasiconformal mappings. In particular, we show that a locally free quasiconformal mapping is globally free quasiconformal under the condition of locally relative quasisymmetry.
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Taxonomy
TopicsAnalytic and geometric function theory · Geometric Analysis and Curvature Flows · Elasticity and Wave Propagation