{"paper":{"title":"Complete stickiness of nonlocal minimal surfaces for small values of the fractional parameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Claudia Bucur, Enrico Valdinoci, Luca Lombardini","submitted_at":"2016-12-25T20:50:27Z","abstract_excerpt":"In this paper, we consider the asymptotic behavior of the fractional mean curvature when $s\\to 0^+$. Moreover, we deal with the behavior of $s$-minimal surfaces when the fractional parameter $s\\in(0,1)$ is small, in a bounded and connected open set with $C^2$ boundary $\\Omega\\subset \\mathbb{R}^n$. We classify the behavior of $s$-minimal surfaces with respect to the fixed exterior data (i.e. the $s$-minimal set fixed outside of $\\Omega$). So, for $s$ small and depending on the data at infinity, the $s$-minimal set can be either empty in $\\Omega$, fill all $\\Omega$, or possibly develop a wildly "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08295","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}