2017/10/24 by Xavier Cabré, Cabre, Xavier, Eleonora Cinti +3
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.1710.08722
openalex publication_date 2017/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
We prove that half spaces are the only stable nonlocal s-minimal cones in ℝ3, for s∈(0,1) sufficiently close to 1. This is the first classification result of stable s-minimal cones in dimension higher than two. Its proof can not rely on a compactness argument perturbing from s=1. In fact, our proof gives a quantifiable value for the required closeness of s to 1. We use the geometric formula for the second variation of the fractional s-perimeter, which involves a squared nonlocal second fundamental form, as well as the recent BV estimates for stable nonlocal minimal sets.