{
  "abstract": "We prove a Bernstein theorem for $Φ$-anisotropic minimal hypersurfaces in dimensions $1\\leq n\\leq 7$ that the only entire smooth solutions $u$ of $Φ$-anisotropic minimal hypersurfaces equation are affine functions provided the anisotropic area functional integrand $Φ$ is sufficiently $C^{2}$--close to the Euclidean area integrand. This settles the $C^2$ entire--graph version of anisotropic Bernstein problem posed by Mooney and Yang \\cite{MooneyYang2024}, and the proof uses a compactness--rigidity argument combined with Figalli's regularity theorem established in \\cite{Figalli2017}.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29117",
  "author_total": 2,
  "authors": [
    {
      "name": "Lu Chen"
    },
    {
      "name": "Jiali Lan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0k7124ycc2cca.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29117",
  "fulltext_url": null,
  "id": "0k7124ycc2cca",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29117",
  "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": "W7204898916",
  "pdf_url": "https://arxiv.org/pdf/2608.29117",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0k7124ycc2cca.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2608.29117",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29117"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A $C^2$-Perturbative Bernstein Theorem for Anisotropic Entire Minimal Graphs",
  "title_text": "A C^2-Perturbative Bernstein Theorem for Anisotropic Entire Minimal Graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/0k7124ycc2cca",
  "venue": "arXiv",
  "versions": []
}