{
  "abstract": "For every dimension $m\\geq 3$, we show the existence of an open set $U\\subset \\mathbb R^{m+1}$, a smooth Riemannian metric $g$ on it, and an integral $m$-dimensional stationary varifold $V$ in $(U,g)$ with the following properties. $V$ has a flat tangent plane of multiplicity $2$ at an interior point $p$, it is a smooth immersed minimal surface in $U\\setminus \\{p\\}$, and it has infinite topology in any neighborhood of $p$. The construction starts from an idea of three of the authors, who in \\cite{DHS} tried to build a similar example with $C^{m-1, α}$ regularity for $g$. That previous attempt contained an important error, which has been overcome using a crucial suggestion of gpt-astra-6.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20647",
  "author_total": 4,
  "authors": [
    {
      "name": "Camillo De Lellis"
    },
    {
      "name": "Jonas Hirsch"
    },
    {
      "name": "Zachary Lihn"
    },
    {
      "name": "Luca Spolaor"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aph8wh629x689.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20647",
  "fulltext_url": null,
  "id": "aph8wh629x689",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20647",
  "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.AP"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7213600707",
  "pdf_url": "https://arxiv.org/pdf/2609.20647",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aph8wh629x689.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.20647",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20647"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Stationary varifolds with singularities II",
  "title_text": "Stationary varifolds with singularities II",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/aph8wh629x689",
  "venue": "arXiv",
  "versions": []
}