{"paper":{"title":"Interpolation and optimal hitting for complete minimal surfaces with finite total curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Antonio Alarcon, Francisco J. Lopez, Ildefonso Castro-Infantes","submitted_at":"2017-12-13T12:14:13Z","abstract_excerpt":"We prove that, given a compact Riemann surface $\\Sigma$ and disjoint finite sets $\\varnothing\\neq E\\subset\\Sigma$ and $\\Lambda\\subset\\Sigma$, every map $\\Lambda \\to \\mathbb{R}^3$ extends to a complete conformal minimal immersion $\\Sigma\\setminus E\\to \\mathbb{R}^3$ with finite total curvature.\n  This result opens the door to study optimal hitting problems in the framework of complete minimal surfaces in $\\mathbb{R}^3$ with finite total curvature. To this respect we provide, for each integer $r\\ge 1$, a set $A\\subset\\mathbb{R}^3$ consisting of $12r+3$ points in an affine plane such that if $A$ i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04727","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"}