Courbure scalaire prescrite sur les variétés Riemanniennes compactes dans le cas négatif

Résumé oblem is proposed of determining functions which are the scalar curvature of some metricg′ conformal to an initial metricg. This problem is equivalent to proving the existence of a function u that is a solution to the equation4(n−1)n−2)Δu+Ru=fu(n+2)/(n−2), u>0.The case of negative scalar curvature is considered here. Sufficient conditions for the proposed equation to have a solution are identified.