{
  "abstract": "We study isolated singularities of positive solutions to a fractional Hartree equation with Riesz interaction, \\[ (-Δ)^s u = \\left( \\int_{\\mathbb{R}^N\\setminus\\{0\\}} \\frac{u^p(y)}{|x-y|^μ}\\,dy \\right)u^q \\quad \\text{in } \\mathbb{R}^N\\setminus\\{0\\}. \\] The puncture changes the passage from the differential equation to its integral form: a fractional fundamental solution term may occur at the singular point. Under an upper bound at the scale of the fundamental solution and a weighted integrability condition on the source, we derive a Riesz decomposition with a nonnegative singular term. Under the same assumptions, if in addition the solution blows up at the puncture, \\(p,q\\ge1\\), and both Kelvin weights are nonnegative, an off-center moving spheres argument yields radial symmetry and strict radial decrease. We also classify positive radial homogeneous singular solutions under the corresponding convergence conditions. If a nonzero positive radial homogeneous scaling limit exists and solves the limiting equation, this classification uniquely determines its coefficient.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Commun. Contemp. Math. 2650079. 2026",
  "arxiv": "2606.10990",
  "author_total": 3,
  "authors": [
    {
      "name": "Guangze Gu"
    },
    {
      "name": "Aleks Jevnikar"
    },
    {
      "name": "Zhipeng Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/edzs65wb880h5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.10990",
  "fulltext_url": null,
  "id": "edzs65wb880h5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.10990",
  "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/2606.10990",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/edzs65wb880h5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2606.10990",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.10990"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Isolated Singularities for Fractional Hartree Equations",
  "title_text": "Isolated Singularities for Fractional Hartree Equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/edzs65wb880h5",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1142/s0219199726500793",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}