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Metrics of constant positive curvature with conic singularities. A survey

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arxiv 2103.13364 v1 pith:SQ4XQMPH submitted 2021-03-24 math.DG math.CAmath.CV

Alexandre Eremenko This is my paper · ORCID
classification math.DGmath.CAmath.CV
keywords singularitiesconicconstantcurvaturemetricsprescribedanglescase
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We consider conformal metrics of constant curvature 1 on a Riemann surface, with finitely many prescribed conic singularities and prescribed angles at these singularities. Especially interesting case which was studied by C. L. Chai, C. S Lin and C. L. Wang is described in some detail, with simplified proofs.

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  1. Existence and uniqueness of solutions to Liouville equation

    math.AP 2025-01 conditional novelty 6.0 of 10

    Sharp existence and uniqueness theorems are proved for the Liouville equation on R^2 with locally integrable or nonnegative potentials, including a comparison principle and radial uniqueness for positive coupling.

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