{
  "abstract": "Let $X:M^n\\to\\mathbb R^{n+1}$ be a complete, connected, two-sided minimal immersion without boundary, where $n=3,4$. We prove that finite $δ$-index, finite Morse index, and finite total curvature are equivalent for $δ>((n-1)/n)^2$, without assumptions on properness, volume growth, or topology. The main estimate shows that $δ$-stability outside a compact set and finite-dimensional $H_c^1(M;\\mathbb R)$ imply intrinsic Euclidean volume growth for $δ>(n-2)/n$. We also deduce the sharp $δ$-stable Bernstein theorem in this latter range from results of Hong--Li--Wang and Florit-Simon.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14317",
  "author_total": 1,
  "authors": [
    {
      "name": "Marcos Ranieri"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9fw34shhse8c5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14317",
  "fulltext_url": null,
  "id": "9fw34shhse8c5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14317",
  "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",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7213292220",
  "pdf_url": "https://arxiv.org/pdf/2609.14317",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9fw34shhse8c5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.14317",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14317"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Minimal hypersurfaces of finite $δ$-index in $\\mathbb R^4$ and $\\mathbb R^5$",
  "title_text": "Minimal hypersurfaces of finite δ-index in ℝ^4 and ℝ^5",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/9fw34shhse8c5",
  "venue": "arXiv",
  "versions": []
}