JournalsrmiVol. 36, No. 5pp. 1333–1374

Teichmüller space of circle diffeomorphisms with Hölder continuous derivatives

  • Katsuhiko Matsuzaki

    Waseda University, Tokyo, Japan
Teichmüller space of circle diffeomorphisms with Hölder continuous derivatives cover

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Abstract

Based on the quasiconformal theory of the universal Teichmüller space, we introduce the Teichmüller space of diffeomorphisms of the unit circle with α\alpha-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+αC^{1+\alpha}-topology at the base point.

Cite this article

Katsuhiko Matsuzaki, Teichmüller space of circle diffeomorphisms with Hölder continuous derivatives. Rev. Mat. Iberoam. 36 (2020), no. 5, pp. 1333–1374

DOI 10.4171/RMI/1169