Journal of Mathematical Analysis and Applications ( IF 1.3 ) Pub Date : 2021-01-20 , DOI: 10.1016/j.jmaa.2021.124975 Shuan Tang , Pengcheng Wu
We introduce and investigate the Teichmüller space of diffeomorphisms of the unit circle with Zygmund continuous derivatives. We first give some characterizations of such diffeomorphism by means of the complex dilatation of its quasiconformal extension and the logarithmic and Schwarzian derivatives of its normalization decomposition. Also, we characterize the quasicircle which corresponds to circle diffeomorphism with Zygmund continuous derivatives by conformal welding. Then, we investigate the logarithmic derivative model and Schwarzian derivative model of Teichmüller space . It is proved that the pre-Bers and Bers projections are holomorphic in and the logarithmic derivative model of is connected in .
中文翻译:
Zygmund光滑圆微分的Teichmüller空间
我们介绍和研究Teichmüller空间 Zygmund连续导数的单位圆的亚纯定性 我们首先通过其准保形扩展的复数扩张以及其归一化分解的对数和Schwarzian导数,对这种亚纯态进行一些表征。此外,我们通过保形焊接来表征与Zygmund连续导数对应的圆微分形的拟圆。然后,我们研究了Teichmüller空间的对数导数模型和Schwarzian导数模型。证明了前Bers和Bers投影是全纯的 和对数导数模型 连接在 。