Asymptotics of the Gaussian Curvatures of the Canonical Metric on the Surface

2006/04/26 by Zheng Huang, Huang, Zheng
Mathematics · #30F60 #32G15 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.CV #math.DG #msc:30F60 #msc:32G15

paper · pdf · doi:10.48550/arxiv.math/0604579

11 pages. A previous post "The Canonical Metric on a Riemann Surface and Its Induced Metric on Teichmüller Space" has been rewritten to two separate papers. This is the one focusing on the canonical metric on a compact Riemann surface

arxiv created 2006/04/26 · openalex publication_date 2006/04/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the canonical metric on a compact Riemann surface of genus at least two. While it is known that the canonical metric is of nonpositive curvature, we show that its Gaussian curvatures are not bounded away from zero nor negative infinity when the surface is close to the compactification divisor of Riemann's moduli space.

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