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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U2 - 10.2140/pjm.2021.314.495

DO - 10.2140/pjm.2021.314.495

M3 - Article

AN - SCOPUS:85119699810

SN - 0030-8730

VL - 314

SP - 495

EP - 514

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

IS - 2

ER -