STABLE s -MINIMAL CONES IN R 3 ARE FLAT FOR s ∼ 1
STABLE s -MINIMAL CONES IN R 3 ARE FLAT FOR s ∼ 1
复制标题
DOI：
--
复制
发表时间：
2019
期刊：
影响因子：
--
通讯作者：
X. Cabré;E. Cinti;J. Serra
中科院分区：
文献类型：
--
作者：
X. Cabré;E. Cinti;J. Serra
. We prove that half spaces are the only stable nonlocal s -minimal cones in R 3 , 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 cannot 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.
