On Teichmüller space of circle diffeomorphisms with Hölder continuous derivative. (English) Zbl 1461.30052
Summary: K. Matsuzaki [Rev. Mat. Iberoam. 36, No. 5, 1333–1374 (2020; Zbl 1468.30075)] introduced the Teichmüller space \(T_0^\alpha\) of diffeomorphisms of the unit circle with Hölder continuous derivatives and investigated its Schwarzian derivative model. This paper deals with the pre-Schwarzian derivative model \(T_0^\alpha (1)\) of the Teichmüller space \(T_0^\alpha\). It is shown that \(T_0^\alpha (1)\) is a connected open subset of \(\mathcal{B}_0^\alpha (\Delta)\) and the pre-Bers projection is a holomorphic split submersion in \(T_0^\alpha\).
MSC:
| 30C62 | Quasiconformal mappings in the complex plane |
| 30F60 | Teichmüller theory for Riemann surfaces |
| 32G15 | Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) |
Citations:
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