{"paper":{"title":"On the Geometry of Rectifiable Sets with Carleson and Poincar\\'e-type Conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Jessica Merhej","submitted_at":"2015-10-17T01:04:31Z","abstract_excerpt":"A central question in geometric measure theory is whether geometric properties of a set translate into analytical ones. In 1960, E. R. Reifenberg proved that if an $n$-dimensional subset $M$ of $\\mathbb{R}^{n+k}$ is well approximated by $n$-planes at every point and at every scale, then $M$ is a locally bi-H\\\"older image of an $n$-plane. Since then, Reifenberg's theorem has been refined in several ways in order to ensure that $M$ is a bi-Lipschitz image of an $n$-plane. In this paper, we show that a Carleson condition on the oscillation of the unit normal of an $n$-Ahlfors regular rectifiable "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05056","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"}