Mingxiang Li

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math.DG2026

A Cheng-Yau type estimate for positive biharmonic functions

Guosheng Jiang, Mingxiang Li, Zhehui Wang

We establish a Cheng-Yau type estimate for positive biharmonic functions on complete Riemannian manifolds with Ricci curvature satisfies $R i c_{g} \geq - (n - 1) K g$ . If $u$ is a positive…

math.DG2026

On the proof of Bray's conjecture

Xumin Jiang, Mingxiang Li, Zhehui Wang

Let $(M^{n}, g)$ be a connected, closed, smooth Riemannian manifold with dimension $n \geq 3$ . There exists a positive constant $ε_{n} < 1$ such that, if Ricci curvature $\operat…

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

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

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

Existence of complete conformal metrics on $R^{n}$ with prescribed Q-curvature

Mingxiang Li, Biao Ma

Given a smooth function $f (x)$ on $R^{n}$ which is positive somewhere and satisfies $f (x) = O (∣ x ∣^{- l})$ for any $l > \frac{n}{2}$ , we show that there exists a complete and conf…

A Cheng-Yau type estimate for positive biharmonic functions

On the proof of Bray's conjecture

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

On the positivity of Yamabe invariant and Paneitz operator

A sharp isoperimetric inequality and the top order Q-curvature

Existence of complete conformal metrics on Rn with prescribed Q-curvature

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

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

Existence of complete conformal metrics on $R^{n}$ with prescribed Q-curvature