2 papers
math.DG2026
Classification of Solutions to a Critical Fourth-Order Equation on Complete Non-compact Manifolds
Huabin Li, Tian Wu, Xiao Zhou
We study the critical biharmonic equation \[ Δ^2 u=u^{\frac{n+4}{n-4}}, \] on a complete, connected, and non-compact Riemannian manifold \((M^n,g)\) of dimension \(n\geq 5\) with n…
math.AP2025
The Liouville-type equation and an Onofri-type inequality on closed 4-manifolds
Xi-Nan Ma, Tian Wu, Xiao Zhou
In this paper, we study the Liouville-type equation \[Δ^2 u-λ_1κΔu+λ_2κ^2(1-\mathrm e^{4u})=0\] on a closed Riemannian manifold \((M^4,g)\) with \(\operatorname{Ric}\geqslant 3κg\)…