{
  "abstract": "We study the linearized Yamabe equation in $\\R^n$, or equivalently on $\\s^n$, at a low-energy sign-changing solution with two nodal domains. We consider odd dimensions $n=2k-1$ and a solution invariant under $Γ=O(k)\\times O(k)$. Its regular level sets are isoparametric hypersurfaces, which foliate the sphere away from the two focal submanifolds. This symmetry reduces the equation for the solution to a singular ODE. In the balanced case, we choose a single-node profile that is odd under reflection across the midpoint. We prove nondegeneracy in the $Γ$-invariant subspace for every $k\\ge2$, and in the full space $H^1(\\s^n)$ for sufficiently large $k$: every kernel element is generated by a conformal invariance of the equation. The proof uses separation of variables, Wronskian identities and comparison functions adapted to the singular equations for the angular modes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40960",
  "author_total": 2,
  "authors": [
    {
      "name": "Sérgio L. N. Neves"
    },
    {
      "name": "Angela Pistoia"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6qt3xp6xwk4x2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40960",
  "fulltext_url": null,
  "id": "6qt3xp6xwk4x2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40960",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40960",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6qt3xp6xwk4x2.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.40960",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40960"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Nondegeneracy of low-energy nodal solutions to the Yamabe equation",
  "title_text": "Nondegeneracy of low-energy nodal solutions to the Yamabe equation",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/6qt3xp6xwk4x2",
  "venue": "arXiv",
  "versions": []
}