{
  "abstract": "This paper continues the study initiated in \\cite{GuJevnikarYang2026b} of fractional Hartree equations with zero capacity singular sets. We are concerned here with the critical case, i.e. \\[ (-Δ)^s u=\\left(\\int_{\\mathbb{R}^N\\setminusΓ} \\frac{u^{2_{μ,s}^*}(y)}{|x-y|^μ}\\,d y\\right)u^{2_{μ,s}^*-1} \\quad\\text{in }\\mathbb{R}^N\\setminusΓ, \\] where $N\\ge2$, $s\\in(0,1)$, $μ\\in(0,N)$ and $2_{μ,s}^*$ is the critical exponent associated to this class of problems. We prove symmetry and monotonicity with respect to the singular set $Γ$. The Kelvin transforms centered at regular points provide sufficient decay at infinity for both the transformed solutions and their associated Hartree coefficients, without imposing global integrability assumptions. Combined with a moving plane argument and a comparison estimate in critical Lebesgue spaces, this allows the moving plane method to cover the full interaction range.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05525",
  "author_total": 3,
  "authors": [
    {
      "name": "Guangze Gu"
    },
    {
      "name": "Aleks Jevnikar"
    },
    {
      "name": "Zhipeng Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cqnje5k9ha0jv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05525",
  "fulltext_url": null,
  "id": "cqnje5k9ha0jv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05525",
  "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"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05525",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cqnje5k9ha0jv.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.05525",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05525"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On symmetry and monotonicity of singular solutions to critical fractional Hartree equations",
  "title_text": "On symmetry and monotonicity of singular solutions to critical fractional Hartree equations",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:29Z",
  "url": "https://research.draconitic.com/paper/cqnje5k9ha0jv",
  "venue": "arXiv",
  "versions": []
}