Horospheres in Teichmüller space and mapping class group

2018/01/05 by Weixu Su, Su, Weixu, Dong Tan +1
Mathematics · #Analytic and geometric function theory #Geometric and Algebraic Topology #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1801.01812

Abstract

We study the geometry of horospheres in Teichmüller space of Riemann surfaces of genus g with n punctures, where 3g-3+n≥ 2. We show that every C¹-diffeomorphism of Teichmüller space to itself that preserves horospheres is an element of the extended mapping class group. Using the relation between horospheres and metric balls, we obtain a new proof of Royden's Theorem that the isometry group of the Teichmüller metric is the extended mapping class group.

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