2009/04/15 by Lixin Liu, Athanase Papadopoulos, Liu, Lixin +5
Mathematics · #30F30 #30F60. #32G15 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #math.GT #msc:30F30 #msc:30F60. #msc:32G15
paper · pdf · doi:10.48550/arxiv.0904.2370
The revised version will appear in Monatshefte für Mathematik
openalex publication_date 2009/04/15 · arxiv created 2009/07/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider some metrics and weak metrics defined on the Teichmueller space of a surface of finite type with nonempty boundary, that are defined using the hyperbolic length spectrum of simple closed curves and of properly embedded arcs, and we compare these metrics and weak metrics with the Teichmüller metric. The comparison is on subsets of Teichmüller space which we call "ε0-relative ε-thick parts", and whose definition depends on the choice of some positive constants ε0 and ε. Meanwhile, we give a formula for the Teichmüller metric of a surface with boundary in terms of extremal lengths of families of arcs.