A convergent Weil-Petersson metric on the Teichmüller space of bordered Riemann surfaces

2014/03/04 by David Radnell, Eric Schippers, Radnell, David +3
Mathematics · #30C62 #32G15 #37F30 #53C56 #81T40 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Geometric and Algebraic Topology #Meromorphic and Entire Functions #Primary 30F60 #Secondary 30C55

paper · pdf · doi:10.48550/arxiv.1403.0868

openalex publication_date 2014/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Σ be a Riemann surface of genus g bordered by n curves homeomorphic to the circle \mathbbS¹, and assume that 2g+2-n>0. For such bordered Riemann surfaces, the authors have previously defined a Teichmüller space which is a Hilbert manifold and which is holomorphically included in the standard Teichmüller space. Based on this, we present alternate models of the aforementioned Teichmüller space and show in particular that it is locally modelled on a Hilbert space of L² Beltrami differentials, which are holomorphic up to a power of the hyperbolic metric, and has a convergent Weil-Petersson metric.

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