{"paper":{"title":"Oka properties of ball complements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Franc Forstneric, Tyson Ritter","submitted_at":"2013-03-09T17:14:50Z","abstract_excerpt":"Let $n>1$ be an integer. We prove that holomorphic maps from Stein manifolds $X$ of dimension $<n$ to the complement $\\mathbb{C}^n\\setminus L$ of a compact convex set $L\\subset\\mathbb{C}^n$ satisfy the basic Oka property with approximation and interpolation. If $L$ is polynomially convex then the same holds when $2\\dim X < n$. We also construct proper holomorphic maps, immersions and embeddings $X\\to\\mathbb{C}^n$ with additional control of the range, thereby extending classical results of Remmert, Bishop and Narasimhan."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.2239","kind":"arxiv","version":7},"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"}