Article ID Journal Published Year Pages File Type
4621344 Journal of Mathematical Analysis and Applications 2008 4 Pages PDF
Abstract

Let (M,g) be a 4-dimensional compact Riemannian manifold and let a,f be positive smooth functions on M. In this note, we prove that the problem Δgu+a(x)u=f(x)u3 always admits a positive solution, up to a conformal deformation of g. This leads to a geometric obstruction result for the prescribed scalar curvature problem.

Related Topics
Physical Sciences and Engineering Mathematics Analysis