{"paper":{"title":"On defining functions for unbounded pseudoconvex domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Giuseppe Tomassini, Nikolay Shcherbina, Tobias Harz","submitted_at":"2014-05-09T14:50:07Z","abstract_excerpt":"We show that every strictly pseudoconvex domain $\\Omega$ with smooth boundary in a complex manifold $\\mathcal{M}$ admits a global defining function, i.e., a smooth plurisubharmonic function $\\varphi \\colon U \\to \\mathbb R$ defined on an open neighbourhood $U \\subset \\mathcal{M}$ of $\\overline{\\Omega}$ such that $\\Omega = \\{\\varphi < 0\\}$, $d\\varphi \\neq 0$ on $b\\Omega$ and $\\varphi$ is strictly plurisubharmonic near $b\\Omega$. We then introduce the notion of the core $\\mathfrak{c}(\\Omega)$ of an arbitrary domain $\\Omega \\subset \\mathcal{M}$ as the set of all points where every smooth and bound"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2250","kind":"arxiv","version":3},"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"}