The Weil-Petersson Geometry On the Thick Part of the Moduli Space of Riemann Surfaces

2006/03/03 by Zheng Huang, Huang, Zheng
Mathematics · #Algebraic Geometry and Number Theory #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.CV #math.DG #msc:30F60 #msc:32G15 #msc:53C21

paper · pdf · doi:10.48550/arxiv.math/0603101

11 pages, a missing reference is added

arxiv created 2006/05/03 · arxiv updated 2009/12/01

Abstract

On the thick part of the moduli space of Riemann surfaces, where there is a positive lower bound of the systole of the surface, we show that all Weil-Petersson Riemannian curvatures are bounded, independent of the genus of the surface.

Citations

• Harmonic Mappings of Riemannian Manifolds

Related

• On Asymptotic Weil-Petersson Geometry of Teichmüller Space of Riemann Surfaces
• Explicit upper bound for the Weil-Petersson volumes
• Asymptotics of the Weil-Petersson metric
• Families of Riemann surfaces and Weil-Petersson geometry
• The vanishing rate of Weil-Petersson sectional curvatures