{"paper":{"title":"Absolute continuity of harmonic measure for domains with lower regular boundaries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Jonas Azzam, Mihalis Mourgoglou, Murat Akman","submitted_at":"2016-05-24T05:22:56Z","abstract_excerpt":"We study absolute continuity of harmonic measure with respect to surface measure on domains $\\Omega$ that have large complements. We show that if $\\Gamma\\subset \\mathbb{R}^{d+1}$ is $d$-Ahlfors regular and splits $ \\mathbb{R}^{d+1}$ into two NTA domains then $\\omega_{\\Omega}\\ll \\mathscr{H}^{d}$ on $\\Gamma\\cap \\partial\\Omega$. This result is a natural generalisation of a result of Wu in [Wu86].\n  We also prove that almost every point in $\\Gamma\\cap\\partial\\Omega$ is a cone point if $\\Gamma$ is a Lipschitz graph. Combining these results and a result from [AHMMMTV], we characterize sets of absolu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07291","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"}