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

Liu, Lixin; Papadopoulos, Athanase; Su, Weixu; Théret, Guillaume

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

Authors

Liu, Lixin

Papadopoulos, Athanase

Su, Weixu

Théret, Guillaume

Description

We define and study metrics and weak metrics on the Teichmueller 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 Teichmueller space which we call $\varepsilon_0$-relative $ε$-thick parts} for $ε>0$ and $\varepsilon_0\geq ε>0$.