Prescribing the scalar curvature problem on higher-dimensional manifolds
Randa Ben Mahmoud Hichem Chtioui
Discrete & Continuous Dynamical Systems - A 2012, 32(5): 1857-1879 doi: 10.3934/dcds.2012.32.1857
In this paper we consider the problem of existence of conformal metrics with prescribed scalar curvature on n-dimensional Riemannian manifolds, $n \geq 5 $. Using precise estimates on the losses of compactness, we characterize the critical points at infinity of the associated variational problem and we prove existence results for curvatures satisfying an assumption of Bahri-Coron type.
keywords: topological method. critical points at infinity Variational method Scalar curvature loss of compactness

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