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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Remarks on prescribing Gauss curvature

Authors: Xingwang Xu and Paul C. Yang
Journal: Trans. Amer. Math. Soc. 336 (1993), 831-840
MSC: Primary 53C21; Secondary 35J60
MathSciNet review: 1087058
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Abstract: We study the nonlinear partial differential equation for the problem of prescribing Gauss curvature $ K$ on $ {S^2}$ . We give an example of a rotationally symmetric $ K$ for which the Kazdan-Warner obstruction is satisfied but the equation has no rotationally symmetric solution. On the other hand, we give a simple sufficient condition for solvability of the equation when $ K$ is rotationally symmetric. Finally we give a sufficient condition for solvability when $ K$ is not necessarily rotationally symmetric.

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