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Prescribing the scalar curvature problem on higher-dimensional manifolds. (English) Zbl 1242.58006
The authors provide existence results for the prescribed scalar curvature problem on a compact Riemannian higher-dimensional manifold. The approach is based on the use of critical points at infinity of an associated functional. An upper bound for the Morse indices of the obtained solutions is also given.
MSC:
58E05Abstract critical point theory
53A30Conformal differential geometry
35J65Nonlinear boundary value problems for linear elliptic equations
53C21Methods of Riemannian geometry, including PDE methods; curvature restrictions (global)
35B40Asymptotic behavior of solutions of PDE