{
  "abstract": "We investigate Bernstein theorem for the affine maximal type equation \\begin{equation*} \\sum_{i,j=1}^nf^{ij}(D^a)_{ij}=0,\\qquad D=\\det(f_{ij}),\\qquad a\\neq0, \\end{equation*} under completeness of the Calabi metric. In dimension two, we prove that every smooth strictly convex solution on a convex domain is a quadratic polynomial whenever $a\\notin[-\\tfrac23,-\\tfrac13]$, resolving a conjecture of Sun and Xu [25]. For every $n\\geq2$, we also construct explicit non-quadratic Calabi complete solutions on convex domains for all $a\\in[-\\tfrac n{n+1},-\\tfrac1{n+1}]$. These examples show that the rigidity range is sharp in dimension two.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05891",
  "author_total": 3,
  "authors": [
    {
      "name": "Yalin Sun"
    },
    {
      "name": "Cheng Xing"
    },
    {
      "name": "Ruiwei Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fan06bq56jvew.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05891",
  "fulltext_url": null,
  "id": "fan06bq56jvew",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05891",
  "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.DG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05891",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fan06bq56jvew.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.05891",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05891"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A sharp Bernstein theorem for affine maximal type surfaces",
  "title_text": "A sharp Bernstein theorem for affine maximal type surfaces",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:30Z",
  "url": "https://research.draconitic.com/paper/fan06bq56jvew",
  "venue": "arXiv",
  "versions": []
}