Mingxiang Li

collaborators

7 papers

math.DG2026

On the positivity of Yamabe invariant and Paneitz operator

Mingxiang Li

Let $(M^{n}, g)$ be a smooth compact Riemannian manifold of dimension $n \geq 5$ . We show that the existence of a conformal metric with positive $Q$ -curvature $Q_{g}$ and positive scalar…

math.DG2026

Bonnet-Myers type theorems for $Q$ -curvature on four-manifolds

Xumin Jiang, Mingxiang Li, Zhehui Wang

Let $(M^{4}, g)$ be a complete four-dimensional Riemannian manifold. First, if the $Q$ -curvature $Q_{g} \geq 6 k^{2}$ and scalar curvature $R_{g} \geq - 12 k$ for some positive constant $k$ , the…

math.DG2026

A sharp isoperimetric inequality and the top order $Q$ -curvature

Mingxiang Li, Xingwang Xu

For a smooth, complete and normal metric $g = e^{2 u} ∣ d x ∣^{2}$ with finite total $n$ -th order $Q$ -curvature on $R^{n}$ with dimension $n \geq 2$ , we first show that everywhere…

math.DG2025

Obstructions to prescribed Q-curvature of complete conformal metrics on $R^{n}$

Mingxiang Li

We provide some obstructions to the prescribed Q-curvature problem for the complete conformal metrics on $R^{n}$ with finite total Q-curvature. One of them is a Bonnet-Mayer…

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…

math.DG2025

Conformal metrics with finite total Q-curvature revisited

Mingxiang Li

Given a conformal metric with finite total Q-curvature, we show that the assumptions on scalar curvature sensitively govern the Q-curvature integral. Additionally, we introduce a c…

On the positivity of Yamabe invariant and Paneitz operator

Bonnet-Myers type theorems for Q-curvature on four-manifolds

A sharp isoperimetric inequality and the top order Q-curvature

Obstructions to prescribed Q-curvature of complete conformal metrics on Rn

On positivity of the Q-curvatures of conformal metrics

Conformal metrics with finite total Q-curvature revisited

Bonnet-Myers type theorems for $Q$ -curvature on four-manifolds

A sharp isoperimetric inequality and the top order $Q$ -curvature

Obstructions to prescribed Q-curvature of complete conformal metrics on $R^{n}$