{"paper":{"title":"Rectifiability and elliptic measures on 1-sided NTA domains with Ahlfors-David regular boundaries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Jos\\'e Mar\\'ia Martell, Matthew Badger, Murat Akman, Steve Hofmann","submitted_at":"2015-07-08T06:32:30Z","abstract_excerpt":"Let $\\Omega \\subset \\mathbb{R}^{n+1}$, $n\\geq 2$, be 1-sided NTA domain (aka uniform domain), i.e. a domain which satisfies interior Corkscrew and Harnack Chain conditions, and assume that $\\partial\\Omega$ is $n$-dimensional Ahlfors-David regular. We characterize the rectifiability of $\\partial\\Omega$ in terms of the absolute continuity of surface measure with respect to harmonic measure. We also show that these are equivalent to the fact that $\\partial\\Omega$ can be covered $\\mathcal{H}^n$-a.e. by a countable union of portions of boundaries of bounded chord-arc subdomains of $\\Omega$ and to t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02039","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"}