Extension of the Weil-Petersson connection

2007/09/16 by Scott A. Wolpert, Wolpert, Scott A. · 1 citation
Mathematics · #30F60 (Secondary) #32G15 (Primary) 20H10 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0709.2513

openalex publication_date 2007/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Convexity properties of Weil-Petersson geodesics on the Teichmüller space of punctured Riemann surfaces are investigated. A normal form is presented for the Weil-Petersson Levi-Civita connection for pinched hyperbolic metrics. The normal form is used to establish approximation of geodesics in boundary spaces. Considerations are combined to establish convexity along Weil-Petersson geodesics of the functions the distance between horocycles for a hyperbolic metric.

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