Xi-nan Ma

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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

Liouville theorem for a class of p-Laplace type equations on manifolds

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

We study a class of $p$ -Laplace equations $Δ_{p} u - λ u^{p - 1} + u^{q - 1} = 0$ on a closed $n$ -dimensional Riemannian manifold $(M, g)$ with $Ric ⩾ (n - 1) g$ . For $1<p<2…

math.AP2024

Best constant and extremal functions for a class Hardy-Sobolev-Maz'ya inequalities

Daowen Lin, Xi-Nan Ma

We derive an integral identity for a class $p$ -Laplace equation, and then classify all positive finite energy cylindrically symmetric solutions of the equation (\ref{1.2}) for $3\l…

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 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

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…

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

Liouville theorem for a class of p-Laplace type equations on manifolds

Best constant and extremal functions for a class Hardy-Sobolev-Maz'ya inequalities

σk​-Yamabe measure

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

$σ_{k}$ -Yamabe measure

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 $R^{n}$