Holomorphic contractibility and other properties of the Weil-Petersson and VMOA Teichmüller spaces

Jinhua Fan, Jun Hu
2016 Annales Academiae Scientiarum Fennicae: Mathematica  
The Weil-Petersson and VMOA Teichmüller spaces, subspaces of the universal Teichmüller space, are complex Banach manifolds modelled on different Banach spaces. We show that they are holomorphically contractible. It is given in [28] that the Kobayashi and Teichmüller metrics coincide with each other on the Weil-Petersson Teichmüller space. We show that this property is also true on the VMOA Teichmüller space. A couple of other properties of the two spaces are also obtained.
doi:10.5186/aasfm.2016.4137 fatcat:fftcdkmx75gdffxi5dmhv2zy4m