Proceedings of the American Mathematical Society

Author(s): A. Eremenko
Journal: Proc. Amer. Math. Soc. 132 (2004), 3349-3355.
MSC (2000): Primary 53C45, 33C05
Posted: April 21, 2004
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Abstract: A simple proof is given of the necessary and sufficient condition on a triple of positive numbers $\theta_1,\theta_2,\theta_3$ for the existence of a conformal metric of constant positive curvature on the sphere, with three conic singularities of total angles $2\pi\theta_1,2\pi\theta_2, 2\pi\theta_3$ . The same condition is necessary and sufficient for the triple $\pi\theta_1,\pi\theta_2,\pi\theta_3$ to be interior angles of a spherical triangular membrane.

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