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

2025/12/10 by Katsuhiko Matsuzaki, Matsuzaki, Katsuhiko
Mathematics · #Analytic and geometric function theory #Holomorphic and Operator Theory #Algebraic and Geometric Analysis

paper · pdf · doi:10.48550/arxiv.2512.09749

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.

Citations

• Integrable Teichmüller spaces for analysis on Weil-Petersson curves
• The complex structure of the Teichmüller space of circle diffeomorphisms in the Zygmund smooth class II
• Simultaneous uniformization of chord-arc curves and BMO Teichmüller space
• BMO embeddings, chord-arc curves, and Riemann mapping parametrization
• Teichmüller space of circle diffeomorphisms with Hölder continuous derivatives

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