Existence of Conformal Metrics with Prescribed Q-Curvature

Abstract EN

We consider the problem of existence of conformal metrics with prescribed Q-curvature on standard sphere Sn,n≥5.

Under the assumption that the order of flatness at critical points of prescribed Q-curvature function K(x) is β ∈ ]1,n−4], we give precise estimates on the losses of the compactness, and we prove new existence and multiplicity results through an Euler-Hopf type formula.