2008/10/31 by Yunping Jiang · 1 citation
Mathematics · #Algebraic and Geometric Analysis #Analytic and geometric function theory #Convex metric space #Equivalence of metrics #Fisher information metric #Geometric and Algebraic Topology #Injective metric space #Intrinsic metric #Metric (unit) #Metric differential #Metric space #Norm (philosophy) #Topology (electrical circuits) #math.CV #math.DS #msc:32H02 #msc:37F99
paper · pdf · doi:10.1007/s11425-019-9520-4
published in Science China Mathematics 62(11), 2249-2270 (Springer Nature)
arxiv created 2009/10/19 · openalex created_date 2016/08/23 · openalex publication_date 2019/05/27 · arxiv updated 2020/06/02 · openalex updated_date 2026/08/05
We introduce a function model for the Teichmüller space of a closed hyperbolic Riemann surface. Then we introduce a new metric by using the maximum norm on the function space on the Teichmüller space. We prove that the identity map from the Teichmüller space equipped with the usual Teichmüller metric to the Teichmüller space equipped with this new metric is uniformly continuous. Furthermore, we also prove that the inverse of the identity, that is, the identity map from the Teichmüller space equipped with this new metric to the Teichmüller space equipped with the usual Teichmüller metric, is continuous. Therefore, the topology induced by the new metric is just the same as the topology induced by the usual Teichmüller metric on the Teichmüller space. We give a remark about the pressure metric and the Weil-Petersson metric.