Almost isometries between Teichmüller spaces

2017/03/08 by Jiang, Manman, Liu, Lixin, Pan, Huiping
#30F60 #32G15 #51F99 #Complex Variables (math.CV) #FOS: Mathematics #Geometric Topology (math.GT) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1703.02687

Abstract

We prove that the Teichmüller space of surfaces with given boundary lengths equipped with the arc metric (resp. the Teichmüller metric) is almost isometric to the Teichmüller space of punctured surfaces equipped with the Thurston metric (resp. the Teichmüller metric).

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