{"paper":{"title":"Accessible parts of the boundary for domains with lower content regular complements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CA"],"primary_cat":"math.MG","authors_text":"Jonas Azzam","submitted_at":"2018-07-12T10:53:48Z","abstract_excerpt":"We show that if $0<t<s\\leq n-1$, $\\Omega\\subseteq \\mathbb{R}^{n}$ with lower $s$-content regular complement, and $z\\in \\Omega$, there is a chord-arc domain $\\Omega_{z}\\subseteq \\Omega $ with center $z$ so that $\\mathscr{H}^{t}_{\\infty}(\\partial\\Omega_{z}\\cap \\partial\\Omega)\\gtrsim_{t} \\textrm{dist}(z,\\Omega^{c})^{t}$. This was originally shown by Koskela, Nandi, and Nicolau with John domains in place of chord-arc domains when $n=2$, $s=1$, and $\\Omega$ is a simply connected planar domain.\n  Domains satisfying the conclusion of this result support $(p,\\beta)$-Hardy inequalities for $\\beta<p-n+t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.04534","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"}