| Abstract: |
| We employ the well-known scalar curvature flow to study the problem of prescribing scalar curvature on $n$-sphere. Assume that the prescribed function $f$, which is allowed to change sign, satisfies certain kind of Morse index counting condition or symmetry condition. We then prove that the scalar curvature flow exists for all time and converges, for a suitable time sequence, to a conformal metric having $f$ as its scalar curvature. As direct consequences, various existence theorems can be derived for the prescribed scalar curvature problem. |
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