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 k is rotationally symmetric. Finally we give a sufficient condition for solvability when K is not necessarily rotationally symmetric.
All Science Journal Classification (ASJC) codes
- General Mathematics
- Applied Mathematics