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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 with nonnegative Ricci curvature.…
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 \(\operatorname{Ric}\geqslant 3κg\)…