{"paper":{"title":"Minimal surfaces in $\\mathbb{R}^3$ properly projecting into $\\mathbb{R}^2$","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":"2009-10-21T16:19:22Z","abstract_excerpt":"For all open Riemann surface M and real number $\\theta \\in (0,\\pi/4),$ we construct a conformal minimal immersion $X=(X_1,X_2,X_3):M \\to \\mathbb{R}^3$ such that $X_3+\\tan(\\theta) |X_1|:M \\to \\mathbb{R}$ is positive and proper. Furthermore, $X$ can be chosen with arbitrarily prescribed flux map.\n  Moreover, we produce properly immersed hyperbolic minimal surfaces with non empty boundary in $\\mathbb{R}^3$ lying above a negative sublinear graph."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.4124","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"}