{
  "abstract": "We study uniqueness of scalar-flat Kähler metrics in a fixed Kähler class on an asymptotically locally Euclidean (ALE) Kähler manifold, assuming only differentiated $o(1)$ decay to a fixed Euclidean metric on the end. In complex dimension $n\\geq2$, under suitable polynomial decay of the reference metric, we prove that the relative Mabuchi functional is finite, continuous, and convex along weak geodesics whose endpoint potentials satisfy $u=O(r^{-γ})$, $γ>2n-4$, together with the corresponding derivative estimates. Combining this convexity with the analysis of the Lichnerowicz operator in weighted spaces, we obtain uniqueness by a perturbation argument. Decay improvement and comparison of the asymptotic charts produce a global potential with the required decay for the difference of the two cohomologous scalar-flat Kähler forms. The argument also extends to asymptotically conical Kähler metrics approaching a fixed Ricci-flat Kähler cone under prescribed decay assumptions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03736",
  "author_total": 1,
  "authors": [
    {
      "name": "Qi Yao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3cms2myywntys.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03736",
  "fulltext_url": null,
  "id": "3cms2myywntys",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03736",
  "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/2611.03736",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3cms2myywntys.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.03736",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03736"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Uniqueness of scalar-flat ALE Kähler metrics",
  "title_text": "Uniqueness of scalar-flat ALE Kähler metrics",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:38Z",
  "url": "https://research.draconitic.com/paper/3cms2myywntys",
  "venue": "arXiv",
  "versions": []
}