Teichmüller space of circle diffeomorphisms with Hölder continuous derivatives

Katsuhiko Matsuzaki

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arXiv · 1607.06300

Teichmüller space of circle diffeomorphisms with Hölder continuous derivatives

Katsuhiko Matsuzaki

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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 $α$-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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BibTeX RIS

Katsuhiko Matsuzaki. 2020-03-29. Teichmüller space of circle diffeomorphisms with Hölder continuous derivatives. https://arxiv.org/abs/1607.06300

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