{"paper":{"title":"Complete minimal surfaces densely lying in arbitrary domains of $\\mathbb{R}^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Antonio Alarcon, Ildefonso Castro-Infantes","submitted_at":"2016-11-15T20:56:38Z","abstract_excerpt":"In this paper we prove that, given an open Riemann surface $M$ and an integer $n\\ge 3$, the set of complete conformal minimal immersions $M\\to\\mathbb{R}^n$ with $\\overline{X(M)}=\\mathbb{R}^n$ forms a dense subset in the space of all conformal minimal immersions $M\\to\\mathbb{R}^n$ endowed with the compact-open topology. Moreover, we show that every domain in $\\mathbb{R}^n$ contains complete minimal surfaces which are dense on it and have arbitrary orientable topology (possibly infinite); we also provide such surfaces whose complex structure is any given bordered Riemann surface.\n  Our method of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.05029","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"}