Teichmüller Spaces Of Piecewise Symmetric Homeomorphisms On The Unit Circle

Huaying Wei; Katsuhiko Matsuzaki

doi:10.2140/pjm.2021.314.495

Teichmüller Spaces Of Piecewise Symmetric Homeomorphisms On The Unit Circle

Huaying Wei^*, Katsuhiko Matsuzaki

^*Corresponding author for this work

School of Education

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

Abstract

We interpolate a new family of Teichmüller spaces T_#^X between the universal Teichmüller space T and its little subspace T₀. Each T_#^X is defined by prescribing a subset X of the unit circle as the exceptional set of the vanishing property for T0. The inclusion relation of X induces a natural inclusion of T_#^X, and an approximation of T by an increasing sequence of T_#^X is investigated. In this paper, we discuss the fundamental properties of T_#^X from the viewpoint of the quasiconformal theory of Teichmüller spaces. We also consider the quotient space of T by T_#^X as an analog of the asymptotic Teichmüller space.

Original language	English
Pages (from-to)	495-514
Number of pages	20
Journal	Pacific Journal of Mathematics
Volume	314
Issue number	2
DOIs	https://doi.org/10.2140/pjm.2021.314.495
Publication status	Published - 2021

Keywords

Bers embedding
asymptotically conformal
barycentric extension
symmetric homeomorphism
universal Teichmüller space

ASJC Scopus subject areas

Mathematics(all)

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10.2140/pjm.2021.314.495

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title = "Teichm{\"u}ller Spaces Of Piecewise Symmetric Homeomorphisms On The Unit Circle",

abstract = "We interpolate a new family of Teichm{\"u}ller spaces T#X between the universal Teichm{\"u}ller space T and its little subspace T0. Each T#X is defined by prescribing a subset X of the unit circle as the exceptional set of the vanishing property for T0. The inclusion relation of X induces a natural inclusion of T#X, and an approximation of T by an increasing sequence of T#X is investigated. In this paper, we discuss the fundamental properties of T#X from the viewpoint of the quasiconformal theory of Teichm{\"u}ller spaces. We also consider the quotient space of T by T#X as an analog of the asymptotic Teichm{\"u}ller space.",

keywords = "Bers embedding, asymptotically conformal, barycentric extension, symmetric homeomorphism, universal Teichm{\"u}ller space",

author = "Huaying Wei and Katsuhiko Matsuzaki",

note = "Funding Information: This research was supported by the National Natural Science Foundation of China (Grant No. 11501259) and the Japan Society for the Promotion of Science (KAKENHI 18H01125). MSC2010: primary 30C62, 30F60, 32G15; secondary 37E10, 58D05. Keywords: universal Teichm{\"u}ller space, symmetric homeomorphism, asymptotically conformal, Bers embedding, barycentric extension. Publisher Copyright: {\textcopyright} 2021, Pacific Journal of Mathematics. All Rights Reserved.",

year = "2021",

doi = "10.2140/pjm.2021.314.495",

language = "English",

volume = "314",

pages = "495--514",

journal = "Pacific Journal of Mathematics",

issn = "0030-8730",

publisher = "University of California, Berkeley",

number = "2",

}

TY - JOUR

T1 - Teichmüller Spaces Of Piecewise Symmetric Homeomorphisms On The Unit Circle

AU - Wei, Huaying

AU - Matsuzaki, Katsuhiko

N1 - Funding Information: This research was supported by the National Natural Science Foundation of China (Grant No. 11501259) and the Japan Society for the Promotion of Science (KAKENHI 18H01125). MSC2010: primary 30C62, 30F60, 32G15; secondary 37E10, 58D05. Keywords: universal Teichmüller space, symmetric homeomorphism, asymptotically conformal, Bers embedding, barycentric extension. Publisher Copyright: © 2021, Pacific Journal of Mathematics. All Rights Reserved.

PY - 2021

Y1 - 2021

N2 - We interpolate a new family of Teichmüller spaces T#X between the universal Teichmüller space T and its little subspace T0. Each T#X is defined by prescribing a subset X of the unit circle as the exceptional set of the vanishing property for T0. The inclusion relation of X induces a natural inclusion of T#X, and an approximation of T by an increasing sequence of T#X is investigated. In this paper, we discuss the fundamental properties of T#X from the viewpoint of the quasiconformal theory of Teichmüller spaces. We also consider the quotient space of T by T#X as an analog of the asymptotic Teichmüller space.

AB - We interpolate a new family of Teichmüller spaces T#X between the universal Teichmüller space T and its little subspace T0. Each T#X is defined by prescribing a subset X of the unit circle as the exceptional set of the vanishing property for T0. The inclusion relation of X induces a natural inclusion of T#X, and an approximation of T by an increasing sequence of T#X is investigated. In this paper, we discuss the fundamental properties of T#X from the viewpoint of the quasiconformal theory of Teichmüller spaces. We also consider the quotient space of T by T#X as an analog of the asymptotic Teichmüller space.

KW - Bers embedding

KW - asymptotically conformal

KW - barycentric extension

KW - symmetric homeomorphism

KW - universal Teichmüller space

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DO - 10.2140/pjm.2021.314.495

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SN - 0030-8730

VL - 314

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EP - 514

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

IS - 2

ER -

Teichmüller Spaces Of Piecewise Symmetric Homeomorphisms On The Unit Circle

Abstract

Keywords

ASJC Scopus subject areas

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