Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 40, 2015, 617-644

ON METRICS DEFINED BY LENGTH SPECTRA ON TEICHMÜLLER SPACES OF SURFACES WITH BOUNDARY

Lixin Liu, Weixu Su and Youliang Zhong

Sun Yat-sen University, Department of Mathematics
510275, Guangzhou, P.R. China; mcsllx 'at' mail.sysu.edu.cn

Fudan University, Department of Mathematics
200433, Shanghai, P.R. China; suwx 'at' fudan.edu.cn

Sun Yat-sen University, Department of Mathematics
510275, Guangzhou, P.R. China; zhongyl0430 'at' gmail.com

Abstract. We prove that the length spectrum metric and the arc-length spectrum metric are almost-isometric on the ε₀-relative part of Teichmüller spaces of surfaces with boundary.

2010 Mathematics Subject Classification: Primary 32G15, 30F30, 30F60.

Key words: Teichmüller space; length spectrum metric; arc-length spectrum metric.

Reference to this article: L. Liu, W. Su and Y. Zhong: On metrics defined by length spectra on Teichmüller spaces of surfaces with boundary. Ann. Acad. Sci. Fenn. Math. 40 (2015), 617-644.

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doi:10.5186/aasfm.2015.4038