Author

S. Alvarez

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Preprint Sep 2026

Stability and uniqueness of minimal disks in non-constant curvature

Nitsche proved that every smooth Jordan curve in $\mathbb{R}^3$ of total curvature at most $4\pi$ bounds a unique minimal disk, which is moreover strictly stable. We prove an analogue of this result for Riemannian $3$-balls with mean convex boundary, under an explicit pinching condition on the negative sectional curvat...

S. Alvarez, Thibault Lefeuvre, Ben Lowe et al. · 0 citations

Preprint Sep 2026

Foliated Plateau problems, surface Radon transforms, and boundary area rigidity in dimension three

The present paper studies integral geometry problems on three-dimensional Riemannian balls, where integration is performed over minimal surfaces or, more generally, $\Phi$-surfaces defined by an elliptic curvature functional $\Phi$. The space of all $\Phi$-surfaces spanned by round circles on the boundary is a three-di...

S. Alvarez, Thibault Lefeuvre, Ben Lowe et al. · 1 citation · ⚡1