{
  "abstract": "Our first main result is a rigidity theorem for complete self-expanders in the Euclidean space with higher codimension, assuming an integral cur More precisely, any smooth complete self-expander $x:M\\to \\mathbb R^{n+p}$($n\\geq3$) that satisfies both $(\\int_{M}|A|^{n}dμ)^{\\frac{1}{n}}<K(n)$ and $\\int_{M}|A|^{n}e^{\\frac{|x|^{2}}{2}}dμ<\\infty$ for a positive constant $K(n)$ depending only o isometric to $\\mathbb R^{n}$. Moreover, we show that the rigidity result persists when the pinching condition is expressed in terms of the trace-free second fundamental form.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20429",
  "author_total": 2,
  "authors": [
    {
      "name": "Zhi Li"
    },
    {
      "name": "Guoxin Wei"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/83y6w8ts5dzp5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20429",
  "fulltext_url": null,
  "id": "83y6w8ts5dzp5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20429",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.20429",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/83y6w8ts5dzp5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.20429",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20429"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The rigidity theorems for complete self-expander of mean curvature flow",
  "title_text": "The rigidity theorems for complete self-expander of mean curvature flow",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/83y6w8ts5dzp5",
  "venue": "arXiv",
  "versions": []
}