Teichmüller space of circle diffeomorphisms with Hölder continuous derivatives

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3 Citations (Scopus)

Abstract

Based on the quasiconformal theory of the universal Teichmüller space, we introduce the Teichmüller space of diffeomorphisms of the unit circle with α-Hölder continuous derivatives as a subspace of the universal Teichmüller space. We characterize such a diffeomorphism quantitatively in terms of the complex dilatation of its quasiconformal extension and the Schwarzian derivative given by the Bers embedding. Then, we provide a complex Banach manifold structure for it and prove that its topology coincides with the one induced by local C1+α-topology at the base point.

Original languageEnglish
Pages (from-to)1333-1374
Number of pages42
JournalRevista Matematica Iberoamericana
Volume36
Issue number5
DOIs
Publication statusPublished - 2020 Feb 10

Keywords

  • Beltrami coefficients
  • Bers embedding
  • Circle diffeomorphism
  • Hölder continuous derivative
  • Quasiconformal map
  • Quasisymmetric homeomorphism
  • Schwarzian derivative
  • Universal Teichmüller space

ASJC Scopus subject areas

  • Mathematics(all)

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