{
  "abstract": "We prove that the local Dirichlet-to-Neumann map of $Δ_g+q$ determines a compact connected real-analytic Riemannian manifold of dimension at least three and a real-analytic real-valued potential, up to a diffeomorphism fixing the observed boundary and the conformal gauge of the equation. The result is new even when \\(q\\) is constant, i.e. for the fixed-frequency (Helmholtz) equation \\(Δ_g u+λu=0\\). The measurements are restricted to an arbitrary nonempty open boundary set $Γ$. The proof develops conformal Poisson embeddings method and uses coordinates given by quotients of solutions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13592",
  "author_total": 4,
  "authors": [
    {
      "name": "Cătălin I. Cârstea"
    },
    {
      "name": "Tony Liimatainen"
    },
    {
      "name": "Yi-Hsuan Lin"
    },
    {
      "name": "William Trad"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ce36yba84d3by.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13592",
  "fulltext_url": null,
  "id": "ce36yba84d3by",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13592",
  "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|Numerical methods in inverse problems"
    ]
  ],
  "openalex": "W7221549637",
  "pdf_url": "https://arxiv.org/pdf/2610.13592",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ce36yba84d3by.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.13592",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13592"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The conformal Poisson embedding method for the anisotropic Calderón problem with a potential",
  "title_text": "The conformal Poisson embedding method for the anisotropic Calderón problem with a potential",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/ce36yba84d3by",
  "venue": "arXiv",
  "versions": []
}