On Teichmüller space of circle diffeomorphisms with Hölder continuous derivative

Abstract

Matsuzaki [M1] 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 \(T_{0}^{\alpha }\).

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Acknowledgements

The authors would like to thank the referee for a very careful reading of the manuscript and for several corrections which greatly improves the presentation of the paper. This work was supported by National Natural Science Foundation of China (Grant No. 12061022).

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Correspondence to Shuan Tang.

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Tang, S., Wu, P. On Teichmüller space of circle diffeomorphisms with Hölder continuous derivative. Anal.Math.Phys. 11, 64 (2021). https://doi.org/10.1007/s13324-021-00502-7

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Keywords

  • Universal Teichmüller space
  • Diffeomorphism
  • Hölder continuous derivative
  • Logarithmic derivative
  • pre-Bers projection

Mathematics Subject Classification

  • Primary 30C62
  • Secondary 30F60
  • 32G15