{"paper":{"title":"Asymptotics of the $s$-perimeter as $s\\searrow 0$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessio Figalli, Enrico Valdinoci, Giampiero Palatucci, Serena Dipierro","submitted_at":"2012-04-03T18:01:50Z","abstract_excerpt":"We deal with the asymptotic behavior of the $s$-perimeter of a set $E$ inside a domain $\\Omega$ as $s\\searrow0$. We prove necessary and sufficient conditions for the existence of such limit, by also providing an explicit formulation in terms of the Lebesgue measure of $E$ and $\\Omega$. Moreover, we construct examples of sets for which the limit does not exist."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.0750","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"}