{"paper":{"title":"Characterizing $W^{2,p}$~submanifolds by $p$-integrability of global curvatures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Heiko von der Mosel, Pawe{\\l} Strzelecki, S{\\l}awomir Kolasi\\'nski","submitted_at":"2012-03-21T09:39:05Z","abstract_excerpt":"We give sufficient and necessary geometric conditions, guaranteeing that an immersed compact closed manifold $\\Sigma^m\\subset \\R^n$ of class $C^1$ and of arbitrary dimension and codimension (or, more generally, an Ahlfors-regular compact set $\\Sigma$ satisfying a mild general condition relating the size of holes in $\\Sigma$ to the flatness of $\\Sigma$ measured in terms of beta numbers) is in fact an embedded manifold of class $C^{1,\\tau}\\cap W^{2,p}$, where $p>m$ and $\\tau=1-m/p$. The results are based on a careful analysis of Morrey estimates for integral curvature--like energies, with integr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.4688","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"}