Accepted Paper

Inserted: 7 dec 2024
Last Updated: 7 apr 2025

Journal: to appear on Nonlinear Analysis
Pages: 16
Year: 2024

Abstract:

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 direct contrast with the case of the classical perimeter or the regime $s$ close to $1$, where nontrivial cones as $\{xy>0\} \subset \mathbb{R}^2$ are stable for inner variations.

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