{"paper":{"title":"Two-dimensional slices of non-pseudoconvex open sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Nikolai Nikolov, Peter Pflug","submitted_at":"2011-03-22T17:39:38Z","abstract_excerpt":"Let $D$ be a non-pseudoconvex open set in $\\C^3$ and $S$ be the union of all two-dimensional planes with non-empty and non-pseudoconvex intersection with $D.$ Sufficient conditions are given for $\\C^3\\setminus S$ to belong to a complex line. Moreover, in the $\\mathcal C^2$-smooth case, it is shown that $S=\\C^n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4323","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"}