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arXiv: 0903.0744

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On length spectrum metrics and weak metrics on Teichmüller spaces of surfaces with boundary

Lixin Liu 1, Athanase Papadopoulos 2, 3, Weixu Su 1, Guillaume Théret 3

(2009-03-04)

We define and study metrics and weak metrics on the Teichmüller space of a surface of topologically finite type with boundary. These metrics and weak metrics are associated to the hyperbolic length spectrum of simple closed curves and of properly embedded arcs in the surface. We give a comparison between the defined metrics on regions of Teichmüller space which we call $\varepsilon_0$-relative $\epsilon$-thick parts} for $\epsilon >0$ and $\varepsilon_0\geq \epsilon>0$.

1:	Department of Mathematics
	Zhongshan University
2:	Institut de Recherche Mathématique Avancée (IRMA)
	CNRS : UMR7501 – Université Louis Pasteur - Strasbourg I
3:	Max-Plank-Institut für Mathematik (MPI)
	Max-Planck-Institut

Subject

:

Mathematics/Geometric Topology

Keyword(s): Teichmüller space – length spectrum metric – length spectrum weak metric – Thurston's asymmetric metric – Teichmüller.

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From: Athanase Papadopoulos <>

Submitted on: Wednesday, 4 March 2009 11:38:17

Updated on: Tuesday, 12 January 2010 21:52:23