22066 articles – 15901 references  [version française]
 HAL: hal-00365704, version 1
 arXiv: 0903.0744
 On length spectrum metrics and weak metrics on Teichmüller spaces of surfaces with boundary
 Lixin Liu 1, Athanase Papadopoulos 2, 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.
Attached file list to this document:
 PS
 boundary.ps(304.9 KB)
 PDF
 boundary.pdf(279.7 KB)
 hal-00365704, version 1 http://hal.archives-ouvertes.fr/hal-00365704 oai:hal.archives-ouvertes.fr:hal-00365704 From: Athanase Papadopoulos <> Submitted on: Wednesday, 4 March 2009 11:38:17 Updated on: Tuesday, 12 January 2010 21:52:23