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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Conformal metrics with prescribed Gaussian curvature on $ S\sp 2$


Authors: Kuo-Shung Cheng and Joel A. Smoller
Journal: Trans. Amer. Math. Soc. 336 (1993), 219-251
MSC: Primary 53C21; Secondary 35A30, 53A30, 58G30
MathSciNet review: 1087053
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Abstract: We consider on $ {S^2}$ the problem of which functions $ K$ can be the scalar curvature of a metric conformal to the standard metric on $ {S^2}$. We assume that $ K$ is a function of one variable, and we obtain a necessary and sufficient condition for the problem to be solvable. We also obtain several new sufficient conditions on $ k$ (which are easy to check), in order that the problem be solvable.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1993-1087053-6
PII: S 0002-9947(1993)1087053-6
Article copyright: © Copyright 1993 American Mathematical Society