{"paper":{"title":"Null Curves in $\\mathbb{C}^3$ and Calabi-Yau Conjectures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Antonio Alarcon, Francisco J. Lopez","submitted_at":"2009-12-15T11:08:49Z","abstract_excerpt":"For any open orientable surface $M$ and convex domain $\\Omega\\subset \\mathbb{C}^3,$ there exists a Riemann surface $N$ homeomorphic to $M$ and a complete proper null curve $F:N\\to\\Omega.$ This result follows from a general existence theorem with many applications. Among them, the followings: For any convex domain $\\Omega$ in $\\mathbb{C}^2$ there exist a Riemann surface $N$ homeomorphic to $M$ and a complete proper holomorphic immersion $F:N\\to\\Omega.$ Furthermore, if $D \\subset \\mathbb{R}^2$ is a convex domain and $\\Omega$ is the solid right cylinder $\\{x \\in \\mathbb{C}^2 | {Re}(x) \\in D\\},$ t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.2847","kind":"arxiv","version":3},"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"}