6 papers · 1 filter
A remark on projection outer volume ratio
A. E. Litvak
We study the projection outer volume ratio introduced by D. Galicer, A.E. Litvak, M. Merzbacher, and D. Pinasco. When , we provide sharp bounds in the…
Noncompactness for the constant -curvature problem
Liuwei Gong, Seunghyeok Kim, Juncheng Wei
For every integer , we construct a fixed smooth, non-locally-conformally-flat metric on the -dimensional unit sphere for which the constant -curvat…
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 -unbounded sequences of positive solutions. The…
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…