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

Lixin Liu, Athanase Papadopoulos, Weixu Su, Guillaume Théret
2010 Annales Academiae Scientiarum Fennicae: Mathematica  
We define and study natural 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 ε 0 -relative -thick parts, for > 0 and ε 0 ≥ > 0. We compare the topologies defined by these metrics on Teichmüller
more » ... ce and we study divergence to infinity with respect to these various metrics.
doi:10.5186/aasfm.2010.3515 fatcat:zyo4iaqp4nbsdmo5hoxnsaaypi