{
  "abstract": "We study overdetermined boundary problems for the maximal surface equation with zero Dirichlet data and constant nonzero Neumann data . For the exterior of a bounded domain with connected boundary in $\\mathbb{R}^n$, $n\\geq2$, we prove that such domain must be the complement of a ball and the solution is radial. In dimension two, we also show that a positive solution on a domain bounded by a properly embedded noncompact connected curve forces the domain to be a half-plane and the solution to be affine. The proofs combine the divergence structure of the equation with the induced geometry of maximal graphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04132",
  "author_total": 1,
  "authors": [
    {
      "name": "Mijia Lai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6bk17d4ms2m1c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04132",
  "fulltext_url": null,
  "id": "6bk17d4ms2m1c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04132",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.DG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04132",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6bk17d4ms2m1c.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.04132",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04132"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Overdetermined boundary problems for maximal graphs",
  "title_text": "Overdetermined boundary problems for maximal graphs",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:38Z",
  "url": "https://research.draconitic.com/paper/6bk17d4ms2m1c",
  "venue": "arXiv",
  "versions": []
}