{
  "abstract": "We prove a growth gap for the gradient of entire anisotropic minimal graphs. For each $n\\geq2$ and each smooth uniformly elliptic parametric integrand $Φ$ on $\\mathbb{R}^{n+1}$, there is an exponent $α=α(n,Φ)>0$ such that every smooth nonaffine entire $Φ$-minimal graph $u:\\mathbb{R}^n\\to\\mathbb{R}$ satisfies $\\sup_{B_R^n}|Du|\\geq cR^α$ for all $R\\geq R_0$, for some constants $c>0$ and $R_0<\\infty$ depending on the solution. In particular, gradient growth $o(R^α)$ forces flatness, resolving a conjecture of Mooney and the author. The result holds in every dimension, without any assumption that $Φ$ is close to the Euclidean area integrand.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08972",
  "author_total": 1,
  "authors": [
    {
      "name": "Yang Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cn33aq14twq4e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08972",
  "fulltext_url": null,
  "id": "cn33aq14twq4e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08972",
  "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"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7212083543",
  "pdf_url": "https://arxiv.org/pdf/2609.08972",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cn33aq14twq4e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:01Z",
      "native_id": "2609.08972",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08972"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A growth gap for anisotropic minimal graphs",
  "title_text": "A growth gap for anisotropic minimal graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:01Z",
  "url": "https://research.draconitic.com/paper/cn33aq14twq4e",
  "venue": "arXiv",
  "versions": []
}