{
  "abstract": "We develop a perturbative theory for minimal submanifolds with only (strongly) isolated singularities, with respect to varying background Riemannian metrics. As an application, we obtain a general \"sporadic persistence\" criterion, thus naturally complementing the non-persistence theorem by the authors. In particular, such a criterion is satisfied by the spherical suspension in $\\mathbb{S}^{3m+2}$ of the Veronese embedding of $\\mathbb{K}\\mathbb{P}^2$ for $\\mathbb{K}=\\mathbb{R},\\mathbb{C},\\mathbb{H},\\mathbb{O}$ (the normed division algebras) in the round spheres of dimension $3m+1=4,7,13,25$ respectively, thereby providing families of continuously varying $(2m+1)$-dimensional stationary varifolds with isolated singularities that are observable on an open set of metrics. By our previous results, these phenomena cannot possibly occur in the codimension one scenario.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22229",
  "author_total": 3,
  "authors": [
    {
      "name": "Alessandro Carlotto"
    },
    {
      "name": "Yangyang Li"
    },
    {
      "name": "Zhihan Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ecpn5a9xgezq4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22229",
  "fulltext_url": null,
  "id": "ecpn5a9xgezq4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22229",
  "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": "W7222497070",
  "pdf_url": "https://arxiv.org/pdf/2610.22229",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ecpn5a9xgezq4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.22229",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22229"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Observing minimal submanifolds with isolated singularities on open sets of metrics",
  "title_text": "Observing minimal submanifolds with isolated singularities on open sets of metrics",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/ecpn5a9xgezq4",
  "venue": "arXiv",
  "versions": []
}