{
  "abstract": "Let $n \\geq 3$. We prove that if $j \\colon (Σ^n,g) \\to (\\mathbb{R}^N,dx^2)$ is an isometric immersion, then \\begin{equation*} \\int_Σ\\left( \\lvert \\nabla u \\rvert^2 + \\frac{n(n-2)}{4}\\lvert H \\rvert^2 u^2 \\right) \\geq \\frac{n(n-2)}{4}\\mathrm{Vol}(S^n)^{2/n}\\left( \\int_Σ\\lvert u \\rvert^{\\frac{2n}{n-2}} \\right)^{\\frac{n-2}{n}} \\end{equation*} for all $u \\in W^{1,2}(Σ)$, and characterize immersions for which equality is realized. Our proof exploits the conformal invariance of the inequality, and hence extends to sharp Michael--Simon inequalities for submanifolds of the sphere, of hyperbolic space, and of other conformally developable manifolds. As an application, we derive Chen--Fenchel--Willmore-type inequalities relating $L^p$-norms of the mean curvature vector to the volume of a compact submanifold of a simply-connected spaceform.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12309",
  "author_total": 2,
  "authors": [
    {
      "name": "Jeffrey S. Case"
    },
    {
      "name": "Dawit Mengesha"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9nc4dpv8frkvn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12309",
  "fulltext_url": null,
  "id": "9nc4dpv8frkvn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12309",
  "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": "W7221193808",
  "pdf_url": "https://arxiv.org/pdf/2610.12309",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9nc4dpv8frkvn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.12309",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12309"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The sharp $L^2$-Michael--Simon inequality",
  "title_text": "The sharp L^2-Michael--Simon inequality",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/9nc4dpv8frkvn",
  "venue": "arXiv",
  "versions": []
}