From best constants to critical functions (Q6275364)

Let \((M,g)\) be a compact Riemannian manifold of dimension \(n\geq 4\) not conformally diffeomorphic to the sphere \(S^n\) and let \(f\) be a smooth function on \(M\). It is shown that there exists a metric conformal to \(g\) for which \(f\) is critical if and only if there exists \(x\in M\) such that \(f(x)>0\).