{
  "abstract": "Nitsche proved that every smooth Jordan curve in $\\mathbb{R}^3$ of total curvature at most $4π$ bounds a unique minimal disk, which is moreover strictly stable. We prove an analogue of this result for Riemannian $3$-balls with mean convex boundary, under an explicit pinching condition on the negative sectional curvature, together with a bound on the covariant derivative of the Ricci tensor. In this setting, every smooth Jordan curve in the boundary sphere of total curvature at most $4π$ bounds a unique embedded minimal disk which is strictly stable.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29542",
  "author_total": 4,
  "authors": [
    {
      "name": "Sébastien Alvarez"
    },
    {
      "name": "Thibault Lefeuvre"
    },
    {
      "name": "Ben Lowe"
    },
    {
      "name": "Graham A. Smith"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dpspzfazjzv0r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29542",
  "fulltext_url": null,
  "id": "dpspzfazjzv0r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29542",
  "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": "W7214394612",
  "pdf_url": "https://arxiv.org/pdf/2609.29542",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dpspzfazjzv0r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.29542",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29542"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Stability and uniqueness of minimal disks in non-constant curvature",
  "title_text": "Stability and uniqueness of minimal disks in non-constant curvature",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/dpspzfazjzv0r",
  "venue": "arXiv",
  "versions": []
}