{
  "abstract": "For the Carlotto–Schulz minimal embeddings of $\\mathbb{S}^{n-1}\\times\\mathbb{S}^{n-1}\\times\\mathbb{S}^1$ in $\\mathbb{S}^{2n}$, we prove uniqueness and nondegeneracy of the normalized monotone closing profile. The first positive Laplace eigenvalue is $2n-1$, and its eigenspace consists of ambient coordinate functions. The full Morse index is $27$ for $n=2$ and $(n^3+9n^2+11n+3)/3$ for $n\\ge3$; the nullity is $n^2+2n$, and every Jacobi field is induced by a rotation. The scalar argument also applies to graphical doubles with unequal spherical factors. Uniqueness for $n\\ge3$ follows from a monotone Jacobi-residual ratio and compact continuation. The kernel theorem gives local rigidity and, for nearby bumpy ambient metrics, minimal hypersurfaces of every index from the base index through that index plus $n^2+2n$. In $\\mathbb{S}^4$ there are at least twenty-one such three-tori.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Anass Nifa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8sqtdtc2eywar.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.22914243",
  "fulltext_url": null,
  "id": "8sqtdtc2eywar",
  "issns": [],
  "landing_url": "https://hal.science/hal-05769981v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-dg"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05769981/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8sqtdtc2eywar.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:43Z",
      "native_id": "hal-05769981",
      "source": "hal",
      "url": "https://hal.science/hal-05769981v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-dg",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Uniqueness, Morse index, and nullity of Carlotto–Schulz minimal hypersurfaces",
  "title_text": "Uniqueness, Morse index, and nullity of Carlotto–Schulz minimal hypersurfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:43Z",
  "url": "https://research.draconitic.com/paper/8sqtdtc2eywar",
  "venue": "HAL",
  "versions": []
}