Prescribing positive curvature with conical singularities on \mathbb S²

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

paper · pdf · doi:10.48550/arxiv.2408.12201

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

Abstract

For conformal metrics with conical singularities and positive curvature on \mathbb S², we prove a convergence theorem and apply it to obtain a criterion for nonexistence in an open region of the prescribing data. The core of our study is a fine analysis of the bubble trees and an area identity in the convergence process.

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