Caculus of Variation and the L²-Bergman Metric on Teichmüller Space

2005/06/28 by Zheng Huang, Huang, Zheng
Mathematics · #30F60 #32G15 #53C21 #Analytic and geometric function theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #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/0506569

16 pages. A missing reference added

openalex publication_date 2005/06/28 · arxiv created 2006/04/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The canonical metric on a Riemann surface is the pullback from the Euclidean metric on the Jacobian variety via the period map. We study its induced L² metric on Teichmuller space via a variational approach.

Citations

• Harmonic Mappings of Riemannian Manifolds

Related

• Survey on the Canonical Metrics on the Teichmüller Spaces and the Moduli Spaces of Riemann Surfaces
• Canonical Metrics on the Moduli Space of Riemann Surfaces II
• A convergent Weil-Petersson metric on the Teichmüller space of bordered Riemann surfaces
• Canonical coordinates and Bergman metrics
• On Teichmuller Space of Surface with Boundary