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Existence of conformal metrics with prescribed Q-curvature on manifolds
Journal article   Peer reviewed

Existence of conformal metrics with prescribed Q-curvature on manifolds

Azeb Alghanemi, Hichem Chtioui and Mohamed Gdarat
Differential geometry and its applications, Vol.85, p.101950
12/2022
DOI: https://doi.org/10.1016/j.difgeo.2022.101950

Abstract

Conformal geometry Critical points at infinity Nonlinear PDE's Q-curvatures
We consider the problem of existence of conformal metrics with prescribed Q-curvature on riemannian n-dimensional manifolds (Mn,g0),5≤n≤7, not conformally diffeomorphic to the standard sphere Sn. Under the assumptions that Qg0 is semi-positive, Rg0 is non-negative and the prescribed function is flat near its critical points, we study the loss of compactness of the problem and we prove existence results through Euler-Hopf type criteria.

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