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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Metrics of positive curvature with conic singularities on the sphere


Author: A. Eremenko
Journal: Proc. Amer. Math. Soc. 132 (2004), 3349-3355
MSC (2000): Primary 53C45, 33C05
Published electronically: April 21, 2004
MathSciNet review: 2073312
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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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Additional Information

A. Eremenko
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email: eremenko@math.purdue.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07439-8
PII: S 0002-9939(04)07439-8
Received by editor(s): May 16, 2003
Received by editor(s) in revised form: July 22, 2003
Published electronically: April 21, 2004
Additional Notes: The author was supported by NSF grant DMS 0100512 and by the Humboldt Foundation
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2004 American Mathematical Society