Spherical metrics with conical singularities on a 2-sphere: angle\n constraints

2015/05/08 by Gabriele Mondello, Mondello, Gabriele, Dmitri Panov +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Algebraic and Geometric Analysis #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.1505.01994

openalex publication_date 2015/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we give a criterion for the existence of a metric of\ncurvature 1 on a 2-sphere with n conical singularities of prescribed\nangles 2\π\ϑ₁,\…,2\π\ϑ_n and non-coaxial holonomy. Such a\nnecessary and sufficient condition is expressed in terms of linear inequalities\nin \ϑ₁,\…,\ϑ_n.\n

Cited by

• Structure and realizability for rational maps

Related

• Geometric structure and existence of reducible spherical conical metrics
• Metrics of constant curvature 1 with three conical singularities on 2-sphere
• Even Cone Spherical Metrics: Blow-Up at a Cone Singularity
• The Nirenberg Problem for Conical Singularities
• Isometric immersions of constant curvature one metrics on the 2-sphere with two conical singularities into Euclidean 3-space: A partial solution to the Gálvez-Hauswirth-Mira problem