Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 41, 2016, 587-600

HOLOMORPHIC CONTRACTIBILITY AND OTHER PROPERTIES OF THE WEIL-PETERSSON AND VMOA TEICHMÜLLER SPACES

Jinhua Fan and Jun Hu

Nanjing University of Science and Technology, Department of Applied Mathematics
Nanjing 210094, P.R. China; jinhuafan 'at' hotmail.com

Brooklyn College of CUNY, Department of Mathematics, Brooklyn, NY 11210, U.S.A.; junhu@brooklyn.cuny.edu
and Graduate Center of CUNY, Ph.D. Program in Mathematics, 365 Fifth Avenue, New York, NY 10016, U.S.A.; JHu1 'at' gc.cuny.edu

Abstract. 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.

2010 Mathematics Subject Classification: Primary 30C75, 30F60.

Key words: Kobayashi metric, Weil-Petersson Teichmüller space, VMOA Teichmüller space, holomorphic contractibility.

Reference to this article: J. Fan and J. Hu: Holomorphic contractibility and other properties of the Weil-Petersson and VMOA Teichmüller spaces. Ann. Acad. Sci. Fenn. Math. 41 (2016), 587-600.

Full document as PDF file

doi:10.5186/aasfm.2016.4137