{"paper":{"title":"An extension theorem of holomorphic functions on hyperconvex domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Seungjae Lee, Yoshikazu Nagata","submitted_at":"2018-11-15T15:48:26Z","abstract_excerpt":"Let $n \\geq 3$ and $\\Omega$ be a bounded domain in $\\mathbb{C}^n$ with a smooth negative plurisubharmonic exhaustion function $\\varphi$. As a generalization of Y. Tiba's result, we prove that any holomorphic function on a connected open neighborhood of the support of $(i\\partial \\bar \\partial \\varphi )^{n-2}$ in $\\Omega$ can be extended to the whole domain $\\Omega$. To prove it, we combine an $L^2$ version of Serre duality and Donnelly-Fefferman type estimates on $(n,n-1)$- and $(n,n)$- forms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.06438","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"}