Author

M. Musso

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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

Preprint Sep 2026

A Supercritical Problem in Dimension Two

Let $\Omega\subset\mathbb R^2$ be a smooth bounded domain containing the origin and invariant under reflection across the coordinate axes, and let $0<\lambda<\lambda_1(\Omega)$, where $\Lambda_1 (\Omega)$ is the first eigenvalue for $-\Delta$ on $\Omega$ under Dirichlet boundary conditions. For every fixed integer $k\g...

M. del Pino, Ignacio A. Guerra, M. Musso · 0 citations