Departmental Bulletin Paper THE ARC METRIC ON TEICHMÜLLER SPACES OF SURFACES OF INFINITE TYPE WITH BOUNDARY

Chen, Qiyu  ,  Liu, Lixin

55 ( 1 )  , pp.1 - 38 , 2018-01 , Osaka University and Osaka City University, Departments of Mathematics
ISSN:00306126
NCID:AA00765910
Description
Let X₀ be a complete hyperbolic surface of infinite type with geodesic boundary which admits a countable pair of pants decomposition. As an application of the Basmajian identity for complete bordered hyperbolic surfaces of infinite type with limit sets of 1-dimensional measure zero, we define an asymmetric metric (which is called arc metric) on the quasiconformal Teichmüller space T(X₀) provided that X₀ satisfies a geometric condition. Furthermore, we construct several examples of hyperbolic surfaces of infinite type satisfying the geometric condition and discuss the relation between the Shiga’s condition and the geometric condition.
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