Author

Liu-Wei Gong

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Preprint Oct 2026

Sharp local scalar-curvature rigidity of spherical caps

Let $B(\delta)\subset\mathbb S^n$ be a geodesic ball with the round metric $\bar{g}$ of sectional curvature one, where $n\geq3$ and $0<\delta<\pi/2$. We prove local scalar-curvature rigidity under preservation of the induced boundary metric and a one-sided lower bound for the boundary mean curvature. More precisely, ev...

Liu-Wei Gong, Jun-Cheng Wei · 0 citations

Preprint Oct 2026

On Critical Dimensions for Compactness in the Boundary Yamabe Problem, II

We determine the sharp compactness ranges for the scalar-flat and minimal-boundary Yamabe problems on smooth compact manifolds of positive conformal type, excluding the conformal round hemisphere. For zero scalar curvature and positive constant boundary mean curvature, compactness holds through dimension $14$ for gener...

Liu-Wei Gong, Seunghyeok Kim, M. Musso et al. · 0 citations

Preprint Sep 2026

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

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 background metric and the prescribed scalar and boundary mean curvatures are fixed along each sequence. For zero scalar curvature and posit...

Liu-Wei Gong, Seunghyeok Kim, M. Musso et al. · 0 citations