Teichmüller space of circle diffeomorphisms with Hölder continuous derivatives

2016/07/21 by Matsuzaki, Katsuhiko · 1 citation
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1607.06300

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 C^1+α-topology at the base point.

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• The real analytic structure of the Teichmüller space of circle diffeomorphisms with Zygmund continuous derivatives

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