Wangzhe Wu

activity

20222026

most citedLiouville theorem for elliptic equations involving the sum of the function and its gradient in

R^{n}

1 citations · 1 across the 12 of their papers we have counts for

collaborators

13 papers

math.DG2026

Rigidity of conformal metrics with constant sixth-order $Q$ -curvature

Daowen Lin, Wangzhe Wu

Let $(M^{n}, g_{0})$ be a closed connected Einstein manifold with positive scalar curvature, where $n \geq 6$ . Using an Obata-type identity, we prove that every smooth metric conformal to…

math.DG2026

A sharp threshold for mixed $Q$ -curvature rigidity

Wangzhe Wu

We resolve Case's question (Crelle's Journal, 2024) on the sharp lower threshold for Obata-type rigidity of $I_{a} = Q + a σ_{2} (A)$ in positive Einstein conformal classes of dimension $n\g…

math.DG2026

Rigidity, sharp inequalities, and stability for $σ_{2}$ -curvature by a reference curvature technique

Wangzhe Wu

Using a reference-curvature technique, we prove four main theorems. (i) For $n \geq 4$ , we remove the mean-curvature pinching from the Case-Wang rigidity theorem for $σ_{2}$ -flat confo…

math.AP2026

Liouville Rigidity and Universal Spacelikeness Estimates for a Lorentzian Prescribed Mean Curvature Equation

Xi-Nan Ma, Tian Wu, Wangzhe Wu +1

We prove a Liouville theorem for nonnegative entire strictly spacelike solutions of \[ \operatorname{div}\left(\frac{\nabla u}{\sqrt{1-|\nabla u|^2}}\right)+u^p=0 \qquad\text{in }\…

math.AP2026

Beyond the $L^{9/5}$ Vorticity Criterion in the Stationary Navier--Stokes Liouville Problem

Wangzhe Wu

Let $(v, p)$ be a smooth stationary Navier--Stokes solution in $R^{3}$ with $v (x) \to 0$ as $∣ x ∣ \to \infty$ . We prove that $v \equiv 0$ if its vorticity $ω := \nabla \times v$ belong…

math.AP2025

Liouville theorem of the subcritical biharmonic equation on complete manifolds

Xi-Nan Ma, Tian Wu, Wangzhe Wu

In this paper, we study the subcritical biharmonic equation \[Δ^2 u=u^α\] on a complete, connected, and non-compact Riemannian manifold $(M^{n}, g)$ with nonnegative Ricci curvature.…

math.AP2025

A remark for characterizing blowup introduced by Giga and Kohn

Wangzhe Wu

Giga and Kohn studied the blowup solutions for the equation $v_{t} - Δ v - ∣ v ∣^{p - 1} v = 0$ and characterized the asymptotic behavior of $v$ near a singularity. In the proof, the…

math.AP2024

$σ_{k}$ -Yamabe measure

Xi-Nan Ma, Wangzhe Wu

We found a special divergence structure for the $σ_{k}$ -Yamabe operator and use it to get a monotonicity formula. We also get an interior $L^{\infty}$ estimate via its $L^{1}$ norm for…

math.AP2023

Liouville theorem for quasilinear elliptic equations in $R^{N}$

Wangzhe Wu, Qiqi Zhang

We prove Liouville theorem for the equation $Δ_{m} v + v^{p} + M ∣\nabla v ∣^{q} = 0$ in a domain $Ω \subset R^{n}$ , with $M \in R$ in the critical and subcritical case. As a…

math.AP2023

Liouville theorem for elliptic equations with a source reaction term involving the product of the function and its gradient in $R^{n}$

Xi-Nan Ma, Wangzhe Wu

We improve the Liouville theorem for the equation $- Δ v = v^{p} ∣\nabla v ∣^{q}$ in $R^{n}$ , which was studied by Bidaut-Véron, García-Huidobro, and Véron. The proof is based on a…

math.AP2023★ 1 cited

Liouville theorem for elliptic equations involving the sum of the function and its gradient in $R^{n}$

Xi-Nan Ma, Wangzhe Wu, Qiqi Zhang

We prove Liouville theorem for the equation $Δ v + N v^{p} + M ∣\nabla v ∣^{q} = 0$ in $R^{n}$ , with $M, N > 0, q = \frac{2 p}{p + 1}$ in the critical and subcritical case. The pro…

math.AP2023

Liouville theorem for one kind of elliptic equations on complete Riemannian manifold

Wangzhe Wu

We use maximum principle to prove the Liouville theorem of the equation $Δ U + b \cdot \nabla U + h U^{α} = 0, U \geq 0, 0 < α < \frac{n + 2}{n - 2}$ on the complete Riemannian manifold…

hep-ph2022

Heavy-quark potential in Gribov-Zwanziger approach around deconfinement phase transition

Wan Wu, Guojun Huang, Jiaxing Zhao +1

The interaction potential between a pair of heavy quarks is calculated with resummed perturbation method in Gribov-Zwanziger approach at finite temperature. The resummed loop corre…

Rigidity of conformal metrics with constant sixth-order Q-curvature

A sharp threshold for mixed Q-curvature rigidity

Rigidity, sharp inequalities, and stability for σ2​-curvature by a reference curvature technique

Liouville Rigidity and Universal Spacelikeness Estimates for a Lorentzian Prescribed Mean Curvature Equation

Beyond the L9/5 Vorticity Criterion in the Stationary Navier--Stokes Liouville Problem

Liouville theorem of the subcritical biharmonic equation on complete manifolds

A remark for characterizing blowup introduced by Giga and Kohn

σk​-Yamabe measure

Liouville theorem for quasilinear elliptic equations in RN

Liouville theorem for elliptic equations with a source reaction term involving the product of the function and its gradient in Rn

Liouville theorem for elliptic equations involving the sum of the function and its gradient in Rn

Liouville theorem for one kind of elliptic equations on complete Riemannian manifold

Heavy-quark potential in Gribov-Zwanziger approach around deconfinement phase transition

Rigidity of conformal metrics with constant sixth-order $Q$ -curvature

A sharp threshold for mixed $Q$ -curvature rigidity

Rigidity, sharp inequalities, and stability for $σ_{2}$ -curvature by a reference curvature technique

Beyond the $L^{9/5}$ Vorticity Criterion in the Stationary Navier--Stokes Liouville Problem

$σ_{k}$ -Yamabe measure

Liouville theorem for quasilinear elliptic equations in $R^{N}$

Liouville theorem for elliptic equations with a source reaction term involving the product of the function and its gradient in $R^{n}$

Liouville theorem for elliptic equations involving the sum of the function and its gradient in $R^{n}$