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On length spectrum metrics and weak metrics on Teichmüller spaces of surfaces with boundary
2010
Annales Academiae Scientiarum Fennicae: Mathematica
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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
doi:10.5186/aasfm.2010.3515
fatcat:zyo4iaqp4nbsdmo5hoxnsaaypi