{
  "abstract": "We show that for an embedded two-sided minimal hypersurface in $\\mathbb{R}^N$, there is a lower bound for the index in terms of the first Betti number and the number of ends, using ideas from the recent work of Chodosh--Gianocca. This estimate is sharp for the higher-dimensional catenoid. We also obtain a $\\operatorname{Spin}(7)$ analogue of Theorem 10.1 of Chodosh--Gianocca: a complete two-sided minimal immersion $M^7\\to\\mathbb{R}^8$ of index one and finite total curvature is a higher-dimensional catenoid.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03424",
  "author_total": 1,
  "authors": [
    {
      "name": "Junzhang Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/98x29xs16bryn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03424",
  "fulltext_url": null,
  "id": "98x29xs16bryn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03424",
  "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": "W7208757194",
  "pdf_url": "https://arxiv.org/pdf/2609.03424",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/98x29xs16bryn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.03424",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03424"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Catenoid-sharp index-topology estimates for minimal hypersurfaces",
  "title_text": "Catenoid-sharp index-topology estimates for minimal hypersurfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/98x29xs16bryn",
  "venue": "arXiv",
  "versions": []
}