4 papers
A counterexample to a strong maximum principle for the sixth-order GJMS operator
Liuwei Gong, Mingxiang Li, Juncheng Wei
We exhibit an explicit closed seven-dimensional Riemannian manifold \[ (M,g)=\mathbb S^2(1)\times \mathbb S^5\left(\frac1{100}\right), \] where the displayed parameters denote sect…
On a new region for the Lane-Emden conjecture in higher dimensions
Kui Li, Mingxiang Li, Juncheng Wei
We study the Lane-Emden conjecture, which asserts the non-existence of non-trivial, non-negative solutions to the Lane-Emden system \[ -Δu = v^p, \quad -Δv = u^q, \quad x \in \math…
On geometry of -curvature
Mingxiang Li, Juncheng Wei, Xingwang Xu
The main purpose of current article is to study the geometry of -curvature. For simplicity, we start with a simple model: a complete and conformal metric on $\m…
A Remark On Case-Gursky-Vétois identity and its applications
Mingxiang Li, Juncheng Wei
Based on the works of Gursky (CMP, 1997), Vétois (Potential Anal., 2023) and Case (Crelle's journal, 2024), we make use of an Obata type formula established in these works to obtai…