Prescribing negative curvature with cusps and conical singularities on compact surface

2024/08/22 by Jingyi Chen, Yuxiang Li, Chen, Jingyi +3
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2408.12195

openalex publication_date 2024/08/22 · openalex created_date 2024/12/20 · openalex updated_date 2026/07/28

Abstract

On a compact surface, we prove existence and uniqueness of the conformal metric whose curvature is prescribed by a negative function away from finitely many points where the metric has prescribed angles presenting cusps or conical singularities.

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