{
  "abstract": "We study the conformal Einstein-Dirac system on the round sphere $S^m$, $m\\geq3$, with coupling coefficient $1+\\eps k$, where $k\\in C^2(S^m,\\R)$ and $\\eps$ is small. Morse and degree conditions yield solutions with positive scalar component, and a generic nondegeneracy condition gives multiplicity modulo spinorial symmetries. For a suitable fixed coefficient, we obtain a noncompact solution sequence with infinitely many distinct energy values. A Kazdan-Warner identity gives nonexistence for a smooth Morse potential and its small $C^2$-perturbations, even with positive coupling. The existence proofs use a local reduction in the interior of the positive cone, accommodating the negative powers occurring when $m\\geq5$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32172",
  "author_total": 3,
  "authors": [
    {
      "name": "Ke Xu"
    },
    {
      "name": "Tian Xu"
    },
    {
      "name": "Minbo Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1thhdbd4ztqqp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32172",
  "fulltext_url": null,
  "id": "1thhdbd4ztqqp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32172",
  "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",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7223687895",
  "pdf_url": "https://arxiv.org/pdf/2610.32172",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1thhdbd4ztqqp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.32172",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32172"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Coupling perturbations of the conformal Einstein-Dirac system on round spheres",
  "title_text": "Coupling perturbations of the conformal Einstein-Dirac system on round spheres",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/1thhdbd4ztqqp",
  "venue": "arXiv",
  "versions": []
}