Spherical Metrics with Conical Singularities on a 2-Sphere: Angle Constraints

Gabriele Mondello; Dmitri Panov

doi:10.1093/imrn/rnv300

Spherical Metrics with Conical Singularities on a 2-Sphere: Angle Constraints

Gabriele Mondello^*, Dmitri Panov

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

35 Citations (Scopus)

Abstract

In this article, we give a criterion for the existence of a metric of curvature 1 on a 2- sphere with nconical singularities of prescribed angles 2πν₁, . . . , 2πν_n and non-coaxial holonomy. Such a necessary and sufficient condition is expressed in terms of linear inequalities in ν₁, . . . , ν_n.

Original language	English
Pages (from-to)	4937-4995
Number of pages	59
Journal	International Mathematics Research Notices
Volume	2016
Issue number	16
Early online date	15 Oct 2015
DOIs	https://doi.org/10.1093/imrn/rnv300
Publication status	Published - 1 Jan 2016

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title = "Spherical Metrics with Conical Singularities on a 2-Sphere: Angle Constraints",

abstract = "In this article, we give a criterion for the existence of a metric of curvature 1 on a 2- sphere with nconical singularities of prescribed angles 2πν1, . . . , 2πνn and non-coaxial holonomy. Such a necessary and sufficient condition is expressed in terms of linear inequalities in ν1, . . . , νn.",

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AB - In this article, we give a criterion for the existence of a metric of curvature 1 on a 2- sphere with nconical singularities of prescribed angles 2πν1, . . . , 2πνn and non-coaxial holonomy. Such a necessary and sufficient condition is expressed in terms of linear inequalities in ν1, . . . , νn.

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Spherical Metrics with Conical Singularities on a 2-Sphere: Angle Constraints

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