{
  "abstract": "Let $C^m \\subset \\mathbb{R}^{m+n}$ be a regular embedded cone, where $n\\geq 1$, and let $k\\geq 1$. We prove that two smooth, connected, properly embedded self-shrinking ends whose blow-downs converge locally smoothly to the same cylindrical cone $C\\times\\mathbb{R}^k$ away from the axis $\\{0\\}\\times\\mathbb{R}^k$ must coincide. As a consequence, we obtain a rigidity result for complete self-shrinkers asymptotic to cylindrical cones. The proof uses Gaussian decay estimates and a sectorial Carleman estimate to establish backward uniqueness.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02303",
  "author_total": 1,
  "authors": [
    {
      "name": "Yile Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d1fcnmjqk4vxg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02303",
  "fulltext_url": null,
  "id": "d1fcnmjqk4vxg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02303",
  "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.DG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02303",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d1fcnmjqk4vxg.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02303",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02303"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Uniqueness of self-shrinking ends asymptotic to a cylindrical cone",
  "title_text": "Uniqueness of self-shrinking ends asymptotic to a cylindrical cone",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/d1fcnmjqk4vxg",
  "venue": "arXiv",
  "versions": []
}