Conformal metrics with prescribed Gaussian curvature on $S^ 2$
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- by Kuo-Shung Cheng and Joel A. Smoller PDF
- Trans. Amer. Math. Soc. 336 (1993), 219-251 Request permission
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.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 336 (1993), 219-251
- MSC: Primary 53C21; Secondary 35A30, 53A30, 58G30
- DOI: https://doi.org/10.1090/S0002-9947-1993-1087053-6
- MathSciNet review: 1087053