The problem of prescribed critical functions

Details The problem of prescribed critical functions The problem of prescribed critical functions

2007-03-23

arxiv.org/abs/math/0703705v1

annals of global analysis 28, No1 (2005) p 19-34

Mathematics

Differential Geometry

Scientific paper

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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