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

Katsuhiko Matsuzaki

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arXiv · 2512.09749

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

Katsuhiko Matsuzaki

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Abstract

We apply the methods of simultaneous uniformization and composition operators on Besov spaces to the Teichmüller space $T^Z$ of circle diffeomorphisms with Zygmund continuous derivatives. As consequences, we obtain the following: (1) a new proof of the correspondence between quasiconformal self-homeomorphisms of the unit disk with complex dilatations of linear decay order and their quasisymmetric extensions to the unit circle with regularity in the Zygmund continuously differentiable class; (2) a real-analytic equivalence of $T^Z$ with the real Banach space of Zygmund continuous functions on the unit circle.

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BibTeX RIS

Katsuhiko Matsuzaki. 2026-09-14. The real analytic structure of the Teichmüller space of circle diffeomorphisms with Zygmund continuous derivatives. https://arxiv.org/abs/2512.09749

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