{
  "abstract": "We prove sharp upper and lower bounds for the Morse index and nullity of linearly full branched minimal 2-spheres in the round 2n-sphere. In particular, we show that the Morse index of a linearly full minimal 2-sphere in the round 2n-sphere is at least n(n-1)(2n+1), with equality if and only if the 2-sphere is twistor-equivalent to the Boruvka sphere. Our techniques also apply more generally to give bounds for the Morse index and nullity for totally isotropic surfaces in the 2n-sphere.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17887",
  "author_total": 2,
  "authors": [
    {
      "name": "Gavin Ball"
    },
    {
      "name": "Jesse Madnick"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6v6p8jqz405vs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17887",
  "fulltext_url": null,
  "id": "6v6p8jqz405vs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17887",
  "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.DG"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
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  "openalex": "W7213524060",
  "pdf_url": "https://arxiv.org/pdf/2609.17887",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6v6p8jqz405vs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.17887",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17887"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The second variation of 2-spheres in the 2n-sphere",
  "title_text": "The second variation of 2-spheres in the 2n-sphere",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/6v6p8jqz405vs",
  "venue": "arXiv",
  "versions": []
}