{
  "abstract": "We study the critical Choquard equation \\[ -Δu-μ|x|^{-2}u =\\bigl(|\\cdot|^{2-N}*|u|^p\\bigr)|u|^{p-2}u \\qquad\\text{in }\\mathbb R^N, \\] where $|\\cdot|^{2-N}$ is the Newton kernel, $p=\\frac{N+2}{N-2}$, and $0<μ<\\frac{(N-2)^2}{4}$. For every $N\\ge3$, we prove that positive solutions in $D^{1,2}(\\mathbb R^N)$ are radially symmetric about the origin, unique up to dilation, and nondegenerate. Our proof uses normalized logarithmic derivatives to obtain a cooperative system. The resulting monotonicity principle underlies both the uniqueness and nondegeneracy arguments, and remains effective in the subquadratic range $1<p<2$, corresponding to $N\\ge7$. Consequently, the linearized quadratic form has Morse index one and the sharp inequality admits a global quadratic remainder estimate. The best constant is strictly concave in the Hardy parameter on $\\bigl[0,\\frac{(N-2)^2}{4}\\bigr)$, is of class $C^2$ with strictly negative second derivative in the interior, and satisfies two-sided bounds that agree to first order at $μ=0$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.08146",
  "author_total": 2,
  "authors": [
    {
      "name": "Guangze Gu"
    },
    {
      "name": "Zhipeng Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0kfzhtfbtdrrn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08146",
  "fulltext_url": null,
  "id": "0kfzhtfbtdrrn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08146",
  "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/2611.08146",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0kfzhtfbtdrrn.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.08146",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08146"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Uniqueness and nondegeneracy for a critical Choquard equation with Hardy potential",
  "title_text": "Uniqueness and nondegeneracy for a critical Choquard equation with Hardy potential",
  "type": "preprint",
  "updated_at": "2026-11-07T18:20:21Z",
  "url": "https://research.draconitic.com/paper/0kfzhtfbtdrrn",
  "venue": "arXiv",
  "versions": []
}