A subscription is required to access this article.
Based on the quasiconformal theory of the universal Teichmüller space, we introduce the Teichmüller space of diffeomorphisms of the unit circle with -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 -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. 1333–1374DOI 10.4171/RMI/1169