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Inserted: 11 nov 2026
Last Updated: 11 nov 2026

Abstract:

Let $\Sigma:=\{(X,Y)\in\mathbb R^4\times\mathbb R^4:
X
=
Y
\}$ be the Simons cone and let $C:=\{
X
\le
Y
\}$. We prove that $C$ minimizes the fractional perimeter $P_s$, under compact perturbations, whenever $s$ is sufficiently close to $1$. The proof constructs two homogeneous families of strict one-sided barriers and converts them into nonlocal sub-calibrations.

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• simons_cone.pdf