{
  "abstract": "We prove a sharp regularity threshold for uniqueness in two anisotropic Calderón-type inverse problems in dimension $n\\ge 3$. The main setting is the Riemannian Schrödinger problem with fixed scalar potential: for a prescribed nonconstant analytic function $V$, we study whether the Dirichlet-to-Neumann map of $-Δ_g+V$ on a domain $Ω\\subset\\mathbb{R}^n$ determines the unknown metric $g$. The natural gauge is the group of boundary-fixing diffeomorphisms preserving $V$. We show that, while analytic metrics are uniquely determined modulo this gauge by a minor adaptation of the Lassas--Uhlmann reconstruction theorem, uniqueness fails densely in every non-analytic Gevrey class $G^σ$, $σ>1$. In fact, our counterexamples are not isometric in the sense that they are not connected by the pushforward of any diffeomorphism of $\\overlineΩ$. We also prove the analogous sharp threshold for the anisotropic Calderón problem at fixed nonzero frequency, thereby upgrading the previously known finite-regularity counterexamples to Gevrey and $C^\\infty$ regularity. The two constructions use different scalar mechanisms: for fixed potentials, the nonconstant potential itself provides a local coordinate, while at nonzero frequency one uses a compactly supported prescribed-Jacobian lemma in Gevrey spaces. Thus analyticity is the exact threshold for uniqueness in both problems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.21705",
  "author_total": 5,
  "authors": [
    {
      "name": "Thierry Daudé"
    },
    {
      "name": "Alberto Enciso"
    },
    {
      "name": "Bernard Helffer"
    },
    {
      "name": "Niky Kamran"
    },
    {
      "name": "François Nicoleau"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/23mzm0e3grfmh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.21705",
  "fulltext_url": null,
  "id": "23mzm0e3grfmh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.21705",
  "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"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2610|Numerical methods in inverse problems"
    ]
  ],
  "openalex": "W7162101751",
  "pdf_url": "https://arxiv.org/pdf/2605.21705",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/23mzm0e3grfmh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2605.21705",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.21705"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A Sharp Regularity Threshold for Uniqueness in Riemannian Calderón-type Problems",
  "title_text": "A Sharp Regularity Threshold for Uniqueness in Riemannian Calderón-type Problems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/23mzm0e3grfmh",
  "venue": "arXiv",
  "versions": []
}