2007/12/31 by Scott A. Wolpert, Wolpert, Scott A. · 4 citations
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.0801.0175
openalex publication_date 2007/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A summary introduction of the Weil-Petersson metric space geometry is presented. Teichmueller space and its augmentation are described in terms of Fenchel-Nielsen coordinates. Formulas for the gradients and Hessians of geodesic-length functions are presented. Applications are considered. A description of the Weil-Petersson metric in Fenchel-Nielsen coordinates is presented. The Alexandrov tangent cone at points of the augmentation is described. A comparison dictionary is presented between the geometry of the space of flat tori and Teichmueller space with the Weil-Petersson metric.