Stable s-minimal cones in ℝ3 are flat for s ~ 1
2020 ◽
Vol 2020
(764)
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pp. 157-180
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Keyword(s):
AbstractWe prove that half spaces are the only stable nonlocal s-minimal cones in {\mathbb{R}^{3}}, for {s\in(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.
2000 ◽
Vol 24
(1)
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pp. 43-48
2009 ◽
Vol 356
(1)
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pp. 237-241
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Keyword(s):
2007 ◽
Vol 463
(2081)
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pp. 1199-1210
1960 ◽
Vol 3
(3)
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pp. 263-271
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2009 ◽
Vol 109A
(2)
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pp. 187-200
Keyword(s):