{"paper":{"title":"Properness of associated minimal surfaces","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":"2012-03-04T17:01:50Z","abstract_excerpt":"We prove that for any open Riemann surface $N$ and finite subset $Z\\subset \\mathbb{S}^1=\\{z\\in\\mathbb{C}\\,|\\;|z|=1\\},$ there exist an infinite closed set $Z_N \\subset \\mathbb{S}^1$ containing $Z$ and a null holomorphic curve $F=(F_j)_{j=1,2,3}:N\\to\\mathbb{C}^3$ such that the map $Y:Z_N\\times N\\to \\mathbb{R}^2,$ $Y(v,P)=Re(v(F_1,F_2)(P)),$ is proper.\n  In particular, $Re(vF):N \\to\\mathbb{R}^3$ is a proper conformal minimal immersion properly projecting into $\\mathbb{R}^2=\\mathbb{R}^2\\times\\{0\\}\\subset\\mathbb{R}^3,$ for all $v \\in Z_N.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.0751","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"}