Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 43, 2018, 365-380

ALMOST ISOMETRIES BETWEEN TEICHMÜLLER SPACES

Manman Jiang, Lixin Liu and Huiping Pan

Guangzhou Maritime University
510725, Guangzhou, P.R. China; jiangmanm 'at' 126.com

Sun Yat-Sen University, School of Mathematics and Computational Science
510275, Guangzhou, P.R. China; mscllx 'at' mail.sysu.edu.cn

Fudan University, School of Mathematical Science
200433, Shanghai, P.R. China; panhp 'at' fudan.edu.cn

Abstract. We prove that the Teichmüller space of hyperbolic surfaces with given boundary lengths equipped with the arc metric (resp. the Teichmüller metric) is almost isometric to the Teichmüller space of punctured surfaces equipped with the Thurston metric (resp. the Teichmüller metric).

2010 Mathematics Subject Classification: Primary 32G15, 30F60, 51F99.

Key words: Teichmüller space, almost isometry, Thurston metric, Teichmüller metric, arc metric.

Reference to this article: M. Jiang, L. Liu and H. Pan: Almost isometries between Teichmüller spaces. Ann. Acad. Sci. Fenn. Math. 43 (2018), 365-380.

Full document as PDF file

https://doi.org/10.5186/aasfm.2018.4320