Stable s-minimal cones in ℝ3 are flat for s ~ 1
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Date
2020-07
Publication Type
Journal Article
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Abstract
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 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. © De Gruyter 2020.
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published
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Journal / series
Volume
764 (2020)
Pages / Article No.
157 - 180
Publisher
De Gruyter