Metrics of positive curvature with conic singularities on the sphere

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/166637A simple proof is given of the necessary and sufficient condition on a triple of positive numbers A,B,C for the existence of a conformal metric of constant positive curvature on the sphere, with three conic singularities of total angles A,B,C. The same condition is necessary and sufficient for the triple A,B,C to be interior angles of a spherical triangular membrane.9 pages, 1 figure, LaTeXMetric GeometryComplex VariablesDifferential Geometry53C45,35J60,33C05Metrics of positive curvature with conic singularities on the spheretext