Revista Matemática Iberoamericana

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Published online first: 2020-02-10
DOI: 10.4171/rmi/1169

Teichmüller space of circle diffeomorphisms with Hölder continuous derivatives

Katsuhiko Matsuzaki[1]

(1) Waseda University, Tokyo, Japan

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

Keywords: Universal Teichmüller space, quasiconformal map, Beltrami coefficients, Schwarzian derivative, Bers embedding, quasisymmetric homeomorphism, circle diffeomorphism, Hölder continuous derivative

Matsuzaki Katsuhiko: Teichmüller space of circle diffeomorphisms with Hölder continuous derivatives. Rev. Mat. Iberoam. Electronically published on February 10, 2020. doi: 10.4171/rmi/1169 (to appear in print)