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 $R^n$ with $n\ge 2m+1$, if the $2m-$order Q-curvature $Q_g^{\left(2m\right)}$ is positive and has slow decay barrier near infinity, the lower order Q-curvature $Q_g^{\left(2\right)}$ and $Q_g^{\left(4\right)}$ are both positive if m is at least two.