{
  "abstract": "We characterize equality in the mass-capacity inequality for asymptotically flat manifolds with arbitrary ends in every dimension \\(n\\ge 3\\). If \\(u\\) is the capacity minimizer, then the equality forces \\((M,u^{4/(n-2)}g)\\) to be isometric to \\((\\mathbb R^n\\setminus S, g_{\\mathrm{Euc}})\\) for a compact set \\(S\\) satisfying \\(\\operatorname{dim}_{\\mathcal H}S\\le (n-2)/2\\). A key ingredient is that conformal changes by positive harmonic functions transform nonnegative Ricci curvature into nonnegative Bakry--Émery Ricci curvature of effective dimension \\(4-n\\).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08579",
  "author_total": 1,
  "authors": [
    {
      "name": "Yuchen Bi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4k68hjfzw684k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08579",
  "fulltext_url": null,
  "id": "4k68hjfzw684k",
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  "landing_url": "https://arxiv.org/abs/2609.08579",
  "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",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7212030390",
  "pdf_url": "https://arxiv.org/pdf/2609.08579",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4k68hjfzw684k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.08579",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08579"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Mass-Capacity Rigidity for Asymptotically Flat Manifolds with Arbitrary Ends",
  "title_text": "Mass-Capacity Rigidity for Asymptotically Flat Manifolds with Arbitrary Ends",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/4k68hjfzw684k",
  "venue": "arXiv",
  "versions": []
}