{"paper":{"title":"On polynomial convexity of compact subsets of totally-real submanifold in $\\mathbb{C}^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Sushil Gorai","submitted_at":"2015-04-27T12:21:50Z","abstract_excerpt":"Let $K$ be a compact subset of a totally-real manifold $M$, where $M$ is either a $\\mathcal{C}^2$-smooth graph in $\\mathbb{C}^{2n}$ over $\\mathbb{C}^n$, or $M=u^{-1}\\{0\\}$ for a $\\mathcal{C}^2$-smooth submersion $u$ from $\\mathbb{C}^n$ to $\\mathbb{R}^{2n-k}$, $k\\leq n$. In this case we show that $K$ is polynomially convex if and only if for a fixed neighbourhood $U$, defined in terms of the defining functions of $M$, there exists a plurisubharmonic function $\\Psi$ on $\\mathbb{C}^n$ such that $K\\subset \\{\\Psi<0\\}\\subset U$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.07049","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"}