{"paper":{"title":"Compactness of the $\\overline{\\partial}$-Neumann operator on the intersection of two domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Emil J. Straube, Mustafa Ayy\\\"ur\\\"u","submitted_at":"2014-08-26T14:48:41Z","abstract_excerpt":"Assume that $\\Omega_{1}$ and $\\Omega_{2}$ are two smooth bounded pseudoconvex domains in $\\mathbb{C}^{2}$ that intersect (real) transversely, and that $\\Omega_{1} \\cap \\Omega_{2}$ is a domain (i.e. is connected). If the $\\overline{\\partial}$-Neumann operators on $\\Omega_{1}$ and on $\\Omega_{2}$ are compact, then so is the $\\overline{\\partial}$-Neumann operator on $\\Omega_{1} \\cap \\Omega_{2}$. The corresponding result holds for the $\\overline{\\partial}$-Neumann operators on $(0,n-1)$-forms on domains in $\\mathbb{C}^{n}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6134","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"}