Asymptotic teichmüller space of a closed set of the riemann sphere

Yi Qi; Yan Wu

doi:10.1090/proc/13144

Asymptotic teichmüller space of a closed set of the riemann sphere

Yi Qi
, Yan Wu^*

^*Corresponding author for this work

School of Mathematical Sciences

Beihang University
Linyi University

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

1 Scopus citations

Abstract

The asymptotic Teichmüller space AT(E) of a closed subset E of the Riemann sphere ℂ with at least 4 points and the natural asymptotic Teichmüller metric are introduced. It is proved that AT(E) is isometrically isomorphic to the product space of the asymptotic Teichmüller spaces of the connected components of ℂ \ E and the Banach space of the Beltrami coeffi- cients defined on E. Furthermore, it is proved that there is a complex Banach manifold structure on AT(E).

Original language	English
Pages (from-to)	2867-2876
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	146
Issue number	7
DOIs	https://doi.org/10.1090/proc/13144
State	Published - Jul 2018

Keywords

Asymptotic Teichmüller space of a closed set
Quasiconformal mapping
Teichmüller space
Teichmüller space of a closed set

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10.1090/proc/13144

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abstract = "The asymptotic Teichm{\"u}ller space AT(E) of a closed subset E of the Riemann sphere ℂ with at least 4 points and the natural asymptotic Teichm{\"u}ller metric are introduced. It is proved that AT(E) is isometrically isomorphic to the product space of the asymptotic Teichm{\"u}ller spaces of the connected components of ℂ \textbackslash{} E and the Banach space of the Beltrami coeffi- cients defined on E. Furthermore, it is proved that there is a complex Banach manifold structure on AT(E).",

keywords = "Asymptotic Teichm{\"u}ller space of a closed set, Quasiconformal mapping, Teichm{\"u}ller space, Teichm{\"u}ller space of a closed set",

author = "Yi Qi and Yan Wu",

note = "Publisher Copyright: {\textcopyright} 2018 American Mathematical Society.",

year = "2018",

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AU - Wu, Yan

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N2 - The asymptotic Teichmüller space AT(E) of a closed subset E of the Riemann sphere ℂ with at least 4 points and the natural asymptotic Teichmüller metric are introduced. It is proved that AT(E) is isometrically isomorphic to the product space of the asymptotic Teichmüller spaces of the connected components of ℂ \ E and the Banach space of the Beltrami coeffi- cients defined on E. Furthermore, it is proved that there is a complex Banach manifold structure on AT(E).

AB - The asymptotic Teichmüller space AT(E) of a closed subset E of the Riemann sphere ℂ with at least 4 points and the natural asymptotic Teichmüller metric are introduced. It is proved that AT(E) is isometrically isomorphic to the product space of the asymptotic Teichmüller spaces of the connected components of ℂ \ E and the Banach space of the Beltrami coeffi- cients defined on E. Furthermore, it is proved that there is a complex Banach manifold structure on AT(E).

KW - Asymptotic Teichmüller space of a closed set

KW - Quasiconformal mapping

KW - Teichmüller space

KW - Teichmüller space of a closed set

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JF - Proceedings of the American Mathematical Society

IS - 7

ER -

Asymptotic teichmüller space of a closed set of the riemann sphere

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Keywords

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