Différentes estimations de \(\sup u\times \inf u\) pour l'équation de la courbure scalaire prescrite en dimension \(n\geqslant 3\). (Various estimates of \(\sup u\times \inf u\) for the equation of prescribed scalar curvature in dimension \(n\geqslant 3\))
The main result of the paper shows that positive solution \(u\) of the equation of prescribed scalar curvature, on a compact set in a Riemannian manifold \((M,g)\), is uniformly bounded. Then, on a compact Riemannian manifold the inequalities \(\sup_M u\times\inf_M u\geq c> 0\) if \(n\geq 3\), \(\sup_M u+\inf_M u\geq c\) if \(n= 2\) are valid.
scientific article; zbMATH DE number 1975975