{
  "abstract": "In this paper, we prove that, for suitable values of $δ$, every complete connected $δ$-Simons stable special Lagrangian immersion in ${\\mathbb C}^n$, $n\\ge3$, is flat. We also prove that a $δ$-Simons stable special Lagrangian cone $C\\subset{\\mathbb C}^n$ with $C\\cap{\\mathbb S}^{2n-1}$ smooth and compact is a finite union of planes if $δ>(n-2)^2/(4n)$, and that this coefficient is optimal. At equality, we characterize the $δ$-Simons stable cones. We further establish regularity and compactness for sequences of proper $δ$-Simons stable special Lagrangian immersions when $n\\ge3$ and $δ>(n-2)/(n+1)$, under suitable restrictions on the initial singular sets, assuming integral current extensions $T_j$ with $\\partial T_j=0$ and uniformly bounded mass on compact subsets. In dimension three, we allow initial singular sets $S_j$ satisfying $\\mathcal H^1(S_j)=0$. For suitable values of $δ$, we also prove properness, Euclidean volume growth, and finite total curvature for complete connected immersions of finite $δ$-index.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.08562",
  "author_total": 1,
  "authors": [
    {
      "name": "Caiyan Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0ete0yrgehptz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08562",
  "fulltext_url": null,
  "id": "0ete0yrgehptz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08562",
  "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/2611.08562",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0ete0yrgehptz.ris",
  "sources": [
    {
      "first_seen": "2026-11-10T06:21:07Z",
      "native_id": "2611.08562",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08562"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Rigidity, Regularity and Compactness of Special Lagrangian Submanifolds under Simons Stability",
  "title_text": "Rigidity, Regularity and Compactness of Special Lagrangian Submanifolds under Simons Stability",
  "type": "preprint",
  "updated_at": "2026-11-10T06:21:07Z",
  "url": "https://research.draconitic.com/paper/0ete0yrgehptz",
  "venue": "arXiv",
  "versions": []
}