Bounded Projective Functions and Hyperbolic Metrics with Isolated Singularities

2017/09/10 by Bo Li, Yu Feng, Li, Bo +5 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #Analytic and geometric function theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1709.03112

openalex publication_date 2017/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish a correspondence on a Riemann surface between hyperbolic metrics with isolated singularities and bounded projective functions whose Schwarzian derivatives have at most double poles and whose monodromies lie in \rm PSU(1, 1). As an application, we construct explicitly a new class of hyperbolic metrics with countably many singularities on the unit disc.

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