{"paper":{"title":"Tangents, rectifiability, and corkscrew domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MG"],"primary_cat":"math.CA","authors_text":"Jonas Azzam","submitted_at":"2015-05-15T04:51:26Z","abstract_excerpt":"In a recent paper, Cs\\\"ornyei and Wilson prove that curves in Euclidean space of $\\sigma$-finite length have tangents on a set of positive $\\mathscr{H}^{1}$-measure. They also show that a higher dimensional analogue of this result is not possible without some additional assumptions. In this note, we show that if $\\Sigma\\subseteq \\mathbb{R}^{d+1}$ has the property that each ball centered on $\\Sigma$ contains two large balls in different components of $\\Sigma^{c}$ and $\\Sigma$ has $\\sigma$-finite $\\mathscr{H}^{d}$-measure, then it has $d$-dimensional tangent points in a set of positive $\\mathscr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03960","kind":"arxiv","version":4},"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"}