{
  "abstract": "We prove that the ground state of the mass-critical Hartree equation is unique up to phase rotations and translations and nondegenerate in every dimension $d\\ge3$. This makes the recent conditional $L^2$ classification of minimal-mass blow-up and non-scattering solutions unconditional; we also give a direct $H^1$ proof of the finite-time blow-up classification. We further establish a global quadratic stability estimate for the sharp Hartree interpolation inequality. For the optimal stability constant, we rule out vanishing of minimizing sequences and describe their possible loss of compactness.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01013",
  "author_total": 2,
  "authors": [
    {
      "name": "Guangze Gu"
    },
    {
      "name": "Zhipeng Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c68627z0h56w4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01013",
  "fulltext_url": null,
  "id": "c68627z0h56w4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01013",
  "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/2611.01013",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c68627z0h56w4.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01013",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01013"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Ground state uniqueness and quantitative stability for the mass-critical Hartree equation",
  "title_text": "Ground state uniqueness and quantitative stability for the mass-critical Hartree equation",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/c68627z0h56w4",
  "venue": "arXiv",
  "versions": []
}