Remarks on Prescribing Gauss Curvature

Xingwang Xu, Paul C. Yang
1993 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