{"paper":{"title":"On the Hartogs extension theorem for unbounded domains in $\\mathbb{C}^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Al Boggess, Egmont Porten, Roman Dwilewicz","submitted_at":"2017-09-11T15:05:56Z","abstract_excerpt":"Let $\\Omega\\subset\\mathbb{C}^n$, $n\\geq 2$, be a domain with smooth connected boundary. If $\\Omega$ is relatively compact, the Hartogs-Bochner theorem ensures that every CR distribution on $\\partial\\Omega$ has a holomorphic extension to $\\Omega$. For unbounded domains this extension property may fail, for example if $\\Omega$ contains a complex hypersurface. The main result in this paper tells that the extension property holds if and only if the envelope of holomorphy of $\\mathbb{C}^n\\backslash\\overline{\\Omega}$ is $\\mathbb{C}^n$. It seems that it is a first result in the literature which gives"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03425","kind":"arxiv","version":1},"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"}