Jännekaarikäyrien avaruus ja Teichmüllerin BMO/VMO-avaruus

Katsuhiko Matsuzaki; Huaying Wei

doi:10.54330/AFM.122367

Jännekaarikäyrien avaruus ja Teichmüllerin BMO/VMO-avaruus

Translated title of the contribution: Space of chord-arc curves and BMO/VMO Teichmüller space

Katsuhiko Matsuzaki^*, Huaying Wei

^*Corresponding author for this work

School of Education

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

Abstract

This paper focuses on the structure of the subspace T_c of the BMO Teichmüller space T_b corresponding to chord-arc curves, which contains the VMO Teichmüller space T_v. We prove that T_c is not a subgroup with respect to the group structure of T_b, but it is preserved under the inverse operation and the left and the right translations by any element of T_v. Moreover, we show that T_b has a fiber structure induced by T_v, and the complex structure of T_b can be projected down to the quotient space T_v\T_b. Then, we see that T_c consists of fibers of this projection, and its quotient space also has the induced complex structure.

Translated title of the contribution	Space of chord-arc curves and BMO/VMO Teichmüller space
Original language	Undefined/Unknown
Pages (from-to)	27-42
Number of pages	16
Journal	Annales Fennici Mathematici
Volume	48
Issue number	1
DOIs	https://doi.org/10.54330/AFM.122367
Publication status	Published - 2022

Keywords

Asymptotic teichmüller space
Bmo teichmüller space
Carleson measure
Chord-arc curve
Quotient bers embedding
Strongly quasisymmetric
Strongly symmetric
Vmo teichmüller space

ASJC Scopus subject areas

Mathematics(all)

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10.54330/AFM.122367

Cite this

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title = "J{\"a}nnekaarik{\"a}yrien avaruus ja Teichm{\"u}llerin BMO/VMO-avaruus",

abstract = "This paper focuses on the structure of the subspace Tc of the BMO Teichm{\"u}ller space Tb corresponding to chord-arc curves, which contains the VMO Teichm{\"u}ller space Tv. We prove that Tc is not a subgroup with respect to the group structure of Tb, but it is preserved under the inverse operation and the left and the right translations by any element of Tv. Moreover, we show that Tb has a fiber structure induced by Tv, and the complex structure of Tb can be projected down to the quotient space Tv\Tb. Then, we see that Tc consists of fibers of this projection, and its quotient space also has the induced complex structure.",

keywords = "Asymptotic teichm{\"u}ller space, Bmo teichm{\"u}ller space, Carleson measure, Chord-arc curve, Quotient bers embedding, Strongly quasisymmetric, Strongly symmetric, Vmo teichm{\"u}ller space",

author = "Katsuhiko Matsuzaki and Huaying Wei",

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year = "2022",

doi = "10.54330/AFM.122367",

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AU - Matsuzaki, Katsuhiko

AU - Wei, Huaying

PY - 2022

Y1 - 2022

N2 - This paper focuses on the structure of the subspace Tc of the BMO Teichmüller space Tb corresponding to chord-arc curves, which contains the VMO Teichmüller space Tv. We prove that Tc is not a subgroup with respect to the group structure of Tb, but it is preserved under the inverse operation and the left and the right translations by any element of Tv. Moreover, we show that Tb has a fiber structure induced by Tv, and the complex structure of Tb can be projected down to the quotient space Tv\Tb. Then, we see that Tc consists of fibers of this projection, and its quotient space also has the induced complex structure.

AB - This paper focuses on the structure of the subspace Tc of the BMO Teichmüller space Tb corresponding to chord-arc curves, which contains the VMO Teichmüller space Tv. We prove that Tc is not a subgroup with respect to the group structure of Tb, but it is preserved under the inverse operation and the left and the right translations by any element of Tv. Moreover, we show that Tb has a fiber structure induced by Tv, and the complex structure of Tb can be projected down to the quotient space Tv\Tb. Then, we see that Tc consists of fibers of this projection, and its quotient space also has the induced complex structure.

KW - Asymptotic teichmüller space

KW - Bmo teichmüller space

KW - Carleson measure

KW - Chord-arc curve

KW - Quotient bers embedding

KW - Strongly quasisymmetric

KW - Strongly symmetric

KW - Vmo teichmüller space

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Jännekaarikäyrien avaruus ja Teichmüllerin BMO/VMO-avaruus

Abstract

Keywords

ASJC Scopus subject areas

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