Liuwei Gong

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20232026

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6 papers · 1 filter

math.DG2026

An ambient metric framework for sharp compactness of the constant $Q_{2 N}$ -curvature problem

Liuwei Gong, Seunghyeok Kim, Juncheng Wei

We develop a geometric method for studying $C^{2 N}$ -compactness of positive solutions to the constant $Q_{2 N}$ -curvature equation on closed Riemannian $n$ -manifolds, for every inte…

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 $Q_{2 N}$ -curvatu…

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.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.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…

An ambient metric framework for sharp compactness of the constant Q2N​-curvature problem

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

Global Convergence of the Gursky-Malchiodi Q-curvature Flow

Oscillatory integral operators on manifolds and related Kakeya and Nikodym problems

An ambient metric framework for sharp compactness of the constant $Q_{2 N}$ -curvature problem

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

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