Injectivity of the quotient Bers embedding of Teichmüller spaces

Katsuhiko Matsuzaki*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

The Bers embedding of the Teichmüller space is a homeomorphism into the Banach space of certain holomorphic automorphic forms. For a subspace of the universal Teichmüller space and its corresponding Banach subspace, we consider whether the Bers embedding can project down between their quotient spaces. If this is the case, it is called the quotient Bers embedding. Injectivity of the quotient Bers embedding is the main problem in this paper. Alternatively, we can describe this situation as the universal Teichmüller space having an affine foliated structure induced by this subspace. We give several examples of subspaces for which the injectivity holds true, including the Teichmüller space of circle diffeomorphisms with Hölder continuous derivative. As an application, the regularity of conjugation between representations of a Fuchsian group into the group of circle diffeomorphisms is investigated.

Original languageEnglish
Pages (from-to)657-679
Number of pages23
JournalAnnales Academiae Scientiarum Fennicae Mathematica
Volume44
Issue number2
DOIs
Publication statusPublished - 2019

Keywords

  • Asymptotic Teichmüller space
  • Asymptotically conformal
  • Bers embedding
  • Circle diffeomorphism
  • Integrable Teichmüller space
  • Quasisymmetric homeomorphism
  • Schwarzian derivative

ASJC Scopus subject areas

  • Mathematics(all)

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