{
  "abstract": "Let $(X^{n+1},g_+)$ be a Poincaré--Einstein manifold with conformal infinity $(M^n,[h])$ of positive Yamabe constant $Y(M,[h])$. Then a relative comparison inequality \\[ \\frac{Y_1(X,M,[\\bar g])}{Y_1(\\mathbb{S}^{n+1}_+,\\mathbb{S}^n,[g_{\\mathbb{S}_+^{n+1}}])} \\geq \\left(\\frac{Y(M,[h])}{Y(\\mathbb{S}^n,[g_{\\mathbb{S}^n}])}\\right)^{\\frac{n}{n+1}} \\] holds for the \\textbf{type-I} Escobar--Yamabe compactification $Y_1(X,M,[\\bar g]$, with equality if and only if $\\left(X, g_{+}\\right)$ is isometric to the hyperbolic space $\\left(\\mathbb{H}^{n+1}, g_{\\mathbb{H}^{n+1}}\\right)$. This confirms a conjecture raised by Sun-Yung A. Chang.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.13742",
  "author_total": 1,
  "authors": [
    {
      "name": "Nan Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1ew8ndvjty1az.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.13742",
  "fulltext_url": null,
  "id": "1ew8ndvjty1az",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.13742",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7168885010",
  "pdf_url": "https://arxiv.org/pdf/2607.13742",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1ew8ndvjty1az.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2607.13742",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.13742"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A sharp relative comparison inequality for conformal fillings of Poincaré--Einstein manifolds",
  "title_text": "A sharp relative comparison inequality for conformal fillings of Poincaré--Einstein manifolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/1ew8ndvjty1az",
  "venue": "arXiv",
  "versions": []
}