The scalar curvature equation on \(S^3\) (Q734345)

Let \(S^3\) be the standard sphere with round metric \(g_0\). The problem studied here is to find the functions K on \(S^3\) which occur as scalar curvature of metrics \(g\) conformally equivalent to \(g_0\). The present paper gives some existence results for solutions of the prescribed scalar curvature equation on \(S^3\), when the curvature function is a positive Morse function and satisfies an index-count condition.