Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 41, 2016, 639-657

THE HILBERT METRIC ON TEICHMÜLLER SPACE AND EARTHQUAKE

Huiping Pan

Sun Yat-Sen University, School of Mathematics and Computational Science
510275, Guangzhou, P.R. China; chnpanhp 'at' foxmail.com

Abstract. Hamenstädt gave a parametrization of the Teichmüller space of punctured surfaces such that the image under this parametrization is the interior of a polytope. In this paper, we study the Hilbert metric on the Teichmüller space of punctured surfaces based on this parametrization. We prove that every earthquake ray is an almost geodesic under the Hilbert metric.

2010 Mathematics Subject Classification: Primary 51F99; Secondary 57N16, 52B70.

Key words: Teichmüller space, Hilbert metric, earthquake, mapping class group.

Reference to this article: H. Pan: The Hilbert metric on Teichmüller space and earthquake. Ann. Acad. Sci. Fenn. Math. 41 (2016), 639-657.

Full document as PDF file

doi:10.5186/aasfm.2016.4144