Teichmüller space of circle diffeomorphisms with Hölder continuous derivatives

• Katsuhiko Matsuzaki ^[1]
  1. [1] Waseda University

     Waseda University

     Japón

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 36, Nº 5, 2020, págs. 1333-1374
• Idioma: inglés
• DOI: 10.4171/rmi/1169
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• Resumen

  • 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.