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arXiv · 2608.21340

Stable $s$-minimal cones in $\mathbb{R}^3$ are flat for $s$ close to zero

Raphael Tsiamis
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Abstract

We prove that stable nonlocal minimal cones in three dimensions are flat, for $s$ sufficiently close to zero. Our approach develops new structural properties of stable $s$-minimal surfaces in every dimension as $s \downarrow 0$, notably a compactness theory and pinching theorems near a half-space.

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Raphael Tsiamis. 2026-08-21. Stable $s$-minimal cones in $\mathbb{R}^3$ are flat for $s$ close to zero. https://arxiv.org/abs/2608.21340

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