5 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…
The (local) geometry of oscillatory integrals on manifolds: Dimension three
Song Dai, Liuwei Gong, Shaoming Guo
Sogge studied Kakeya problems on two extreme types of three dimensional Riemannian manifolds: Manifolds with the most symmetries (manifolds of constant sectional curvature) and man…
Global Convergence of the Gursky-Malchiodi -curvature Flow
Liuwei Gong, Sanghoon Lee, Juncheng Wei
In their seminal work, Gursky and Malchiodi introduced a non-local conformal flow in dimensions to resolve the constant -curvature problem. They proved sequential con…
Compactness and non-compactness theorems of the fourth- and sixth-order constant -curvature problems
Liuwei Gong, Seunghyeok Kim, Juncheng Wei
We provide a complete resolution to the question of compactness for the full solution sets of the fourth-order and sixth-order constant -curvature problems on smooth closed Riem…
Conformal metrics of constant scalar curvature with unbounded volumes
Liuwei Gong, Yanyan Li
For , we construct a smooth metric on the standard -dimensional sphere such that there exists a sequence of smooth metrics $\{\tilde{g}_k\}_…