Xingwang Xu

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math.DG2025

On geometry of $Q_{g}^{(2 k)}$ -curvature

Mingxiang Li, Juncheng Wei, Xingwang Xu

The main purpose of current article is to study the geometry of $Q$ -curvature. For simplicity, we start with a simple model: a complete and conformal metric $g = e^{2 u} ∣ d x ∣^{2}$ on $\m…

math.DG2025

On positivity of the Q-curvatures of conformal metrics

Mingxiang Li, Xingwang Xu

We mainly show that for a conformal metric $g = u^{\frac{4}{n - 2 m}} ∣ d x ∣^{2}$ on $R^{n}$ with $n \geq 2 m + 1$ , if the higher order Q-curvature $Q_{g}^{(2 m)}$ is positive and has slow d…

On geometry of Qg(2k)​-curvature

On positivity of the Q-curvatures of conformal metrics

On geometry of $Q_{g}^{(2 k)}$ -curvature