Liuwei Gong

activity

20232026

collaborators

9 papers

math.FA2026

A remark on projection outer volume ratio

A. E. Litvak

We study the projection outer volume ratio $povr_{k} (K)$ introduced by D. Galicer, A.E. Litvak, M. Merzbacher, and D. Pinasco. When $k \leq n /2$ , we provide sharp bounds in the…

math.DG2026

Noncompactness for the constant $Q_{2 N}$ -curvature problem

Liuwei Gong, Seunghyeok Kim, Juncheng Wei

For every integer $N \geq 4$ , we construct a fixed smooth, non-locally-conformally-flat metric on the $n$ -dimensional unit sphere $S^{n}$ for which the constant $Q_{2 N}$ -curvat…

math.DG2026

On critical dimensions for compactness in the boundary Yamabe problem, I

Liuwei Gong, Seunghyeok Kim, Monica Musso +1

We construct smooth, non-locally-conformally-flat metrics on the closed ball for which the boundary Yamabe equation admits $L^{\infty}$ -unbounded sequences of positive solutions. The…

math.DG2026

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…

math.CA2026

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…

math.DG2026

Global Convergence of the Gursky-Malchiodi $Q$ -curvature Flow

Liuwei Gong, Sanghoon Lee, Juncheng Wei

In their seminal work, Gursky and Malchiodi introduced a non-local conformal flow in dimensions $n \geq 5$ to resolve the constant $Q$ -curvature problem. They proved sequential con…

math.AP2025

Compactness and non-compactness theorems of the fourth- and sixth-order constant $Q$ -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 $Q$ -curvature problems on smooth closed Riem…

math.AP2024

Conformal metrics of constant scalar curvature with unbounded volumes

Liuwei Gong, Yanyan Li

For $n \geq 25$ , we construct a smooth metric $g ~$ on the standard $n$ -dimensional sphere $S^{n}$ such that there exists a sequence of smooth metrics $\{\tilde{g}_k\}_…

math.DG2023

Oscillatory integral operators on manifolds and related Kakeya and Nikodym problems

Song Dai, Liuwei Gong, Shaoming Guo +1

We consider Carleson-Sjölin operators on Riemannian manifolds that arise naturally from the study of Bochner-Riesz problems on manifolds. They are special cases of Hörmander-type o…

A remark on projection outer volume ratio

Noncompactness for the constant Q2N​-curvature problem

On critical dimensions for compactness in the boundary Yamabe problem, I

A counterexample to a strong maximum principle for the sixth-order GJMS operator

The (local) geometry of oscillatory integrals on manifolds: Dimension three

Global Convergence of the Gursky-Malchiodi Q-curvature Flow

Compactness and non-compactness theorems of the fourth- and sixth-order constant Q-curvature problems

Conformal metrics of constant scalar curvature with unbounded volumes

Oscillatory integral operators on manifolds and related Kakeya and Nikodym problems

Noncompactness for the constant $Q_{2 N}$ -curvature problem

Global Convergence of the Gursky-Malchiodi $Q$ -curvature Flow

Compactness and non-compactness theorems of the fourth- and sixth-order constant $Q$ -curvature problems