Abstract
We show that the only nonlocal s-minimal cones in \({\mathbb{R}^2}\) are the trivial ones for all \({s \in (0, 1).}\) As a consequence we obtain that the singular set of a nonlocal minimal surface has at most n − 3 Hausdorff dimension.
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Communicated by L. Ambrosio.
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Savin, O., Valdinoci, E. Regularity of nonlocal minimal cones in dimension 2. Calc. Var. 48, 33–39 (2013). https://doi.org/10.1007/s00526-012-0539-7
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DOI: https://doi.org/10.1007/s00526-012-0539-7