Stable s-minimal cones in ℝ² are flat for s ∼ 0

2024/12/09 by Caselli, Michele
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2412.06318

Abstract

For s ∈ (0,1) small, we show that the only cones in ℝ² stationary for the s-perimeter and stable in ℝ² ∖ \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\ ⊂ ℝ² are stable for inner variations.

Related

• Stable s-minimal cones in ℝ³ are flat for s∼ 1
• Regularity of nonlocal minimal cones in dimension 2
• Sliding minimal cones in the 3-dimensional half-space
• Measure and sliding stability for 2-dimensional minimal cones in Euclidean spaces
• Regularity for minimal sets near a union of two planes