{
  "abstract": "We prove local rigidity of smooth conformally Euclidean metrics $g_0$ on smooth compact domains $M\\subset\\mathbb{R}^n$, $n\\ge3$, for the anisotropic Helmholtz equation $(-Δ_g -k^2)u =0$ at a fixed energy $k^2>0$ which is not a Dirichlet eigenvalue of $-Δ_{g_0}$ in $M$. Any smooth metric sufficiently close to $g_0$ in $H^s(M)$, with integer $s>n/2+1$, and having the same Dirichlet-to-Neumann map, is its pullback by a smooth diffeomorphism fixing the boundary pointwise. The proof uses a Helmholtz embedding to fix the gauge and a compactness argument together with a characterization of the kernel of the linearization.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25314",
  "author_total": 2,
  "authors": [
    {
      "name": "Sebastián Muñoz-Thon"
    },
    {
      "name": "Plamen Stefanov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7f5k3ggpn0t32.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25314",
  "fulltext_url": null,
  "id": "7f5k3ggpn0t32",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25314",
  "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",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7223063508",
  "pdf_url": "https://arxiv.org/pdf/2610.25314",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7f5k3ggpn0t32.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.25314",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25314"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Local rigidity of conformally Euclidean metrics for the anisotropic Helmholtz equation at fixed energy",
  "title_text": "Local rigidity of conformally Euclidean metrics for the anisotropic Helmholtz equation at fixed energy",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/7f5k3ggpn0t32",
  "venue": "arXiv",
  "versions": []
}