Stable $s$-minimal cones in ${\mathbb{R}}^2$ are flat for $s\sim 0$

Michele Caselli

For $s\in (0,1)$ small, we show that the only cones in ${\mathbb{R}}^2$ stationary for the $s$-perimeter and stable in ${\mathbb{R}}^2\setminus \{0\}$ are half-planes. This is in dir…