A note on Väisälä’s problem concerning free quasiconformal mappings

Qingshan Zhou; Yaxiang Li; Antti Rasila

doi:10.1007/s00605-021-01554-4

A note on Väisälä’s problem concerning free quasiconformal mappings

Qingshan Zhou, Yaxiang Li, Antti Rasila^*

^*Corresponding author for this work

Mathematics with Computer Science

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In this paper, we provide partial solutions to a problem raised by Väisälä on local properties of free quasiconformal mappings. In particular, we show that a locally free quasiconformal mapping is a globally free quasiconformal mapping under the condition of locally relative quasisymmetry.

Original language	English
Pages (from-to)	607-616
Number of pages	10
Journal	Monatshefte fur Mathematik
Volume	196
Issue number	3
DOIs	https://doi.org/10.1007/s00605-021-01554-4
State	Published - Nov 2021

Keywords

Free quasiconformal mapping
Quasihyperbolic metric
Quasisymmetric mapping

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10.1007/s00605-021-01554-4

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title = "A note on V{\"a}is{\"a}l{\"a}{\textquoteright}s problem concerning free quasiconformal mappings",

abstract = "In this paper, we provide partial solutions to a problem raised by V{\"a}is{\"a}l{\"a} on local properties of free quasiconformal mappings. In particular, we show that a locally free quasiconformal mapping is a globally free quasiconformal mapping under the condition of locally relative quasisymmetry.",

keywords = "Free quasiconformal mapping, Quasihyperbolic metric, Quasisymmetric mapping",

author = "Qingshan Zhou and Yaxiang Li and Antti Rasila",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature.",

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AU - Zhou, Qingshan

AU - Li, Yaxiang

AU - Rasila, Antti

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AB - In this paper, we provide partial solutions to a problem raised by Väisälä on local properties of free quasiconformal mappings. In particular, we show that a locally free quasiconformal mapping is a globally free quasiconformal mapping under the condition of locally relative quasisymmetry.

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KW - Quasihyperbolic metric

KW - Quasisymmetric mapping

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JO - Monatshefte fur Mathematik

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A note on Väisälä’s problem concerning free quasiconformal mappings

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Keywords

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