Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 43, 2018, 935-943

WEIL–PETERSSON AND LITTLE TEICHMÜLLER SPACES ON THE REAL LINE

Yuliang Shen, Shuan Tang and Li Wu

Soochow University, Department of Mathematics
Suzhou 215006, P.R. China; ylshen 'at' suda.edu.cn

Guizhou Normal University, School of Mathematics Sciences
Guiyang 550001, P.R. China; tsa 'at' gznu.edu.cn

Soochow University, Department of Mathematics
Suzhou 215006, P.R. China; wuli187 'at' 126.com

Abstract. We will prove that an increasing homeomorphism h in the Weil–Petersson class on the real line must be locally absolutely continuous such that log h' belongs to the Sobolev class H^1/2. We will also deal with the the pre-logarithmic derivative models of the little and Weil–Petersson Teichmüller spaces in the half plane case.

2010 Mathematics Subject Classification: Primary 30C62, 30F60, 32G15.

Key words: Universal Teichmüller space, little Teichmüller space, Weil–Petersson Teichmüller space, Weil–Petersson class, quasiconformal mapping, Sobolev class.

Reference to this article: Y. Shen, S. Tang and L. Wu: Weil–Petersson and little Teichmüller spaces on the real line. Ann. Acad. Sci. Fenn. Math. 43 (2018), 935-943.

Full document as PDF file

https://doi.org/10.5186/aasfm.2018.4358