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The problem of prescribed critical functions

Emmanuel Humbert·Michel Vaugon
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Abstract

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

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Emmanuel Humbert, Michel Vaugon. 2007-03-23. The problem of prescribed critical functions. https://arxiv.org/abs/math/0703705

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