{
  "abstract": "We complete, in the general Riemannian setting, the classification of isolated singularities of positive solutions to the Yamabe equation for dimensions \\(3\\le n\\le29\\), initiated in the flat case by Caffarelli, Gidas, and Spruck in 1989. Precisely, every isolated singularity is either removable or the solution is asymptotic to a Fowler solution. The sharpness of this range is established by counterexamples for every dimension \\(n\\ge30\\) in our companion paper.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28323",
  "author_total": 5,
  "authors": [
    {
      "name": "Zheng-Chao Han"
    },
    {
      "name": "Qinfeng Jiang"
    },
    {
      "name": "Hua-Yang Wang"
    },
    {
      "name": "Jingang Xiong"
    },
    {
      "name": "Lei Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5yca3kev2bt5t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28323",
  "fulltext_url": null,
  "id": "5yca3kev2bt5t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28323",
  "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"
    ],
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      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7214203928",
  "pdf_url": "https://arxiv.org/pdf/2609.28323",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5yca3kev2bt5t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2609.28323",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28323"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Isolated singularities of solutions to the Yamabe equation in higher dimensions I",
  "title_text": "Isolated singularities of solutions to the Yamabe equation in higher dimensions I",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/5yca3kev2bt5t",
  "venue": "arXiv",
  "versions": []
}