Author

Davide Parise

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Preprint Oct 2026

Regularity and compactness theory of stable free-boundary minimal hypersurfaces

We establish the free-boundary version of Schoen-Simon's regularity and compactness theory for stable minimal hypersurfaces in a complete $(n+1)$-dimensional Riemannian manifold-with-boundary, following the intrinsic PDE scheme introduced by the first-named author. The key step is to prove sheeting theorems in the two...

C. Bellettini, M. Li, Davide Parise et al. · 0 citations

Preprint Sep 2026

Uniqueness of free boundary minimal annuli

We prove that every smooth properly embedded free-boundary minimal annulus in the unit ball is congruent to the critical catenoid. We also classify positive solutions of $(\Delta_{\mathbb{S}^2}+2)u=0$ on smooth spherical annuli with $u=0$ and $|\nabla u|=1$ on the boundary; their one-homogeneous extensions are the axia...

Davide Parise, Jonathan J. Zhu · 1 citation