{"paper":{"title":"Approximation of a Reifenberg-flat set by a smooth surface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Guy David (LM-Orsay)","submitted_at":"2012-11-14T07:30:31Z","abstract_excerpt":"We show that if $E \\i \\R^n$ is a Reifenberg flat set $E$ of dimension $d$ at scale $r_0$, we can find a smooth surface $\\Sigma_0$ of dimension $d$ which is close to $E$ at the scale $r_0$. When $E$ is a Reifenberg flat set, this allows us to apply a result of G. David and T. Toro [Memoirs of the AMS 215 (2012), 1012], and get a bi-H\\\"older homeomorphism of $\\R^n$ that sends $\\Sigma_0$ to $E$. If in addition $d=n-1$ and $E$ is compact and connected, then $\\Sigma_0$ is orientable, and $\\R^n \\sm E$ has exactly two connected components, which we can approximate from the inside by smooth domains."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3222","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"}