{"paper":{"title":"Sharp Boundedness and Regularizing effects of the integral Menger curvature for submanifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.FA","authors_text":"Simon Blatt, S{\\l}awomir Kolasi\\'nski","submitted_at":"2011-10-21T13:27:31Z","abstract_excerpt":"In this paper we show that embedded and compact $C^1$ manifolds have finite integral Menger curvature if and only if they are locally graphs of certain Sobolev-Slobodeckij spaces. Furthermore, we prove that for some intermediate energies of integral Menger type a similar characterization of objects with finite energy can be given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4786","kind":"arxiv","version":1},"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"}