Deformations of Riemann Surfaces

2014/10/26 by Jörg Winkelmann, Winkelmann, Jörg
Mathematics · #30F20 #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.CV #msc:30F20

paper · pdf · doi:10.48550/arxiv.1410.7086

15 pages

arxiv created 2014/10/26 · openalex publication_date 2014/10/26 · arxiv updated 2014/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that every Riemann surface not isomorphic to the Riemann sphere admits an infinitesimal deformation of the complex structure. The proof is based in an investigation of the length of geodesics for the Kobayashi/Poincare metric.

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