Teichmüller Spaces Of Piecewise Symmetric Homeomorphisms On The Unit Circle

Huaying Wei*, Katsuhiko Matsuzaki

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)495-514
Number of pages20
JournalPacific Journal of Mathematics
Issue number2
Publication statusPublished - 2021


  • Bers embedding
  • asymptotically conformal
  • barycentric extension
  • symmetric homeomorphism
  • universal Teichmüller space

ASJC Scopus subject areas

  • Mathematics(all)


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