{
  "abstract": "We classify any entire area-minimizing surface $M^2\\subset\\mathbb{R}^n$ with density $2$ at infinity as either planar, or the zero set of a quadratic holomorphic polynomial inside some affine copy of $\\mathbb{C}^2$. We also prove algebraicity of $M^2$ when the tangent cone at infinity has multiplicity one with general density. In our proof we introduce a sheeting-type theorem for minimizing surfaces near a multiplicity-two plane at infinity, and a new proof of holomorphicity (different from \\cite{micallef}) based on a general ``calibrated at infinity'' principle.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.15795",
  "author_total": 3,
  "authors": [
    {
      "name": "Nick Edelen"
    },
    {
      "name": "Luis Atzin Franco Reyna"
    },
    {
      "name": "Paul Minter"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7b8q3kvayacd3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.15795",
  "fulltext_url": null,
  "id": "7b8q3kvayacd3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.15795",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7164930871",
  "pdf_url": "https://arxiv.org/pdf/2606.15795",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7b8q3kvayacd3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2606.15795",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.15795"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Entire area-minimizing surfaces in $\\mathbf{R}^n$ of density two are quadratic or planar",
  "title_text": "Entire area-minimizing surfaces in R^n of density two are quadratic or planar",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/7b8q3kvayacd3",
  "venue": "arXiv",
  "versions": []
}