The paper claims that for small values of the fractional perimeter parameter s, the only stable s-minimal cones in R^2 are half-planes, but a key integral estimate in the proof is false.
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Stable $s$-minimal cones in $\mathbb{R}^2$ are flat for $s \sim 0$
The paper claims that for small values of the fractional perimeter parameter s, the only stable s-minimal cones in R^2 are half-planes, but a key integral estimate in the proof is false.