{"paper":{"title":"Compact complete null curves in Complex 3-space","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":"2011-06-03T15:13:31Z","abstract_excerpt":"We prove that for any open orientable surface $S$ of finite topology, there exist a Riemann surface $\\mathcal{M},$ a relatively compact domain $M\\subset\\mathcal{M}$ and a continuous map $X:\\bar{M}\\to\\mathbb{C}^3$ such that: $\\mathcal{M}$ and $M$ are homeomorphic to $S,$ $\\mathcal{M}-M$ and $\\mathcal{M}-\\bar{M}$ contain no relatively compact components in $\\mathcal{M},$ $X|_M$ is a complete null holomorphic curve, $X|_{\\bar{M}-M}:\\bar{M}-M\\to\\mathbb{C}^3$ is an embedding and the Hausdorff dimension of $X(\\bar{M}-M)$ is $1.$\n  Moreover, for any $\\epsilon>0$ and compact null holomorphic curve $Y:"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0684","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"}