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arXiv · 2609.29542

Stability and uniqueness of minimal disks in non-constant curvature

Sébastien Alvarez·Thibault Lefeuvre·Ben Lowe·Graham A. Smith
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Abstract

Nitsche proved that every smooth Jordan curve in $\mathbb{R}^3$ of total curvature at most $4π$ 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 curvature, together with a bound on the covariant derivative of the Ricci tensor. In this setting, every smooth Jordan curve in the boundary sphere of total curvature at most $4π$ bounds a unique embedded minimal disk which is strictly stable.

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Sébastien Alvarez, Thibault Lefeuvre, Ben Lowe, Graham A. Smith. 2026-09-24. Stability and uniqueness of minimal disks in non-constant curvature. https://arxiv.org/abs/2609.29542

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