{"paper":{"title":"A construction of complete complex hypersurfaces in the ball with control on the topology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CV","authors_text":"Antonio Alarcon, Francisco J. Lopez, Josip Globevnik","submitted_at":"2015-09-08T08:32:32Z","abstract_excerpt":"Given a closed complex hypersurface $Z\\subset \\mathbb{C}^{N+1}$ $(N\\in\\mathbb{N})$ and a compact subset $K\\subset Z$, we prove the existence of a pseudoconvex Runge domain $D$ in $Z$ such that $K\\subset D$ and there is a complete proper holomorphic embedding from $D$ into the unit ball of $\\mathbb{C}^{N+1}$. For $N=1$, we derive the existence of complete properly embedded complex curves in the unit ball of $\\mathbb{C}^2$, with arbitrarily prescribed finite topology. In particular, there exist complete proper holomorphic embeddings of the unit disc $\\mathbb{D}\\subset \\mathbb{C}$ into the unit b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02283","kind":"arxiv","version":2},"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"}