{
  "abstract": "Let $(M^n,\\mathfrak g)$, $3\\le n\\le7$, be a one-ended asymptotically flat manifold whose boundary $Σ$ is a connected, strictly stable, outermost minimal hypersurface. As $p\\downarrow1$, the $p$-capacity of $Σ$ converges to its area, by a theorem of Fogagnolo and Mazzieri. We establish a higher-order asymptotic expansion governed by a single function on $Σ$: the positive solution $g$ of the reciprocal Jacobi equation $Jg=g^{-1}$. After a universal term, the first correction is determined by the average of $\\log g$, and the capacitary potential drops from one to zero across a Gaussian boundary layer of width $g\\sqrt{p-1}$; under the normalized energy measure, the logarithm of the gradient has limiting variance $\\frac12$ plus the variance of $\\log g$. In dimension three, assuming in addition that $R_{\\mathfrak g}+|\\mathrm{II}|^2\\ge0$ along $Σ$, we identify the capacity deficit of $Σ$ relative to the Schwarzschild horizon of the same area at order $p-1$: it is nonnegative, vanishes exactly when the induced metric of $Σ$ is round and $R_{\\mathfrak g}+|\\mathrm{II}|^2\\equiv0$, and controls the deviation of $g$ from a constant through a relative-entropy identity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25444",
  "author_total": 1,
  "authors": [
    {
      "name": "Sehong Park"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7bd8fxrsvwcb4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25444",
  "fulltext_url": null,
  "id": "7bd8fxrsvwcb4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25444",
  "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": "W7223019528",
  "pdf_url": "https://arxiv.org/pdf/2610.25444",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7bd8fxrsvwcb4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.25444",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25444"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Endpoint capacity at strictly stable minimal boundaries:Gaussian layers and Schwarzschild deficits",
  "title_text": "Endpoint capacity at strictly stable minimal boundaries:Gaussian layers and Schwarzschild deficits",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/7bd8fxrsvwcb4",
  "venue": "arXiv",
  "versions": []
}