Vol. 314, No. 2, 2021

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Teichmüller spaces of piecewise symmetric homeomorphisms on the unit circle

Huaying Wei and Katsuhiko Matsuzaki

Vol. 314 (2021), No. 2, 495–514
Abstract

We interpolate a new family of Teichmüller spaces TX between the universal Teichmüller space T and its little subspace T0. Each TX 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 TX, and an approximation of T by an increasing sequence of TX is investigated. In this paper, we discuss the fundamental properties of TX from the viewpoint of the quasiconformal theory of Teichmüller spaces. We also consider the quotient space of T by TX as an analog of the asymptotic Teichmüller space.

Keywords
universal Teichmüller space, symmetric homeomorphism, asymptotically conformal, Bers embedding, barycentric extension
Mathematical Subject Classification 2010
Primary: 30C62, 30F60, 32G15
Secondary: 37E10, 58D05
Milestones
Received: 26 December 2019
Revised: 16 December 2020
Accepted: 14 August 2021
Published: 10 November 2021
Authors
Huaying Wei
Department of Mathematics and Statistics
Jiangsu Normal University
Xuzhou
China
Katsuhiko Matsuzaki
Department of Mathematics
School of Education
Waseda University
Tokyo
Japan