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Remarks on Prescribing Gauss Curvature
Transactions of the American Mathematical Society
We study the nonlinear partial differential equation for the problem of prescribing Gauss curvature K on S2 . 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 A" is rotationally symmetric. Finally we give a sufficient condition for solvability when K is not necessarily rotationally symmetric.doi:10.2307/2154378 fatcat:g4ow7wyssvbrdcq56d7me75ete