On positivity of the Q-curvatures of conformal metrics

Abstract

We mainly show that for a conformal metric $g=u^{\frac{4}{n-2m}}|dx{|}^2$ on ${\mathbb{R}}^n$ with $n\ge 2m+1$, if the higher order Q-curvature $Q_g^{(2m)}$ is positive and has slow decay barrier near infinity, the lower order Q-curvature $Q_g^{(2)}$ and $Q_g^{(4)}$ are both positive if $m$ is at least two.

20 pages. Published version in JFA

References in corpus (1)

• Existence and non-existence results for the higher order Hardy-Hénon equation revisited