The problem of prescribed critical functions

Emmanuel Humbert (1) , Michel Vaugon (2)

1 IECN - Institut Élie Cartan de Nancy
2 IMJ - Institut de Mathématiques de Jussieu

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 $f(x)>0$.

Mots clés: Sobolev inequalities

Mots clés: Best constants; Sobolev inequalities.

Domaines: Géométrie différentielle [math.DG]

Emmanuel Humbert, Michel Vaugon. The problem of prescribed critical functions. annals of global analysis, 2005, 28, No1, p 19-34. ⟨10.1007/s10455-005-1583-8⟩. ⟨hal-00138196⟩