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 (2)

1 Department of Mathematics
2 MPI - Max-Planck-Institut für Mathematik
3 IRMA - Institut de Recherche Mathématique Avancée

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 $\varepsilon_0\geq \epsilon>0$.

Mots clés: Teichmüller; Teichmüller space; length spectrum weak metric; length spectrum metric; Thurston's asymmetric metric; Teichmüller.

Domaines: Topologie géométrique [math.GT]

Lixin Liu, Athanase Papadopoulos, Weixu Su, Guillaume Théret. On length spectrum metrics and weak metrics on Teichmüller spaces of surfaces with boundary. 2009. ⟨hal-00365704⟩