{
  "abstract": "We study an inverse boundary value problem for the Helmholtz equation on a smooth compact non-trapping Riemannian manifold with strictly convex boundary. We prove that, given two such metrics, for sufficiently large but fixed frequency $λ$, equality of their Dirichlet-to-Neumann maps implies equality of their lens data, up to a smooth boundary-fixing diffeomorphism. This establishes a high-frequency bridge between the Calderón problem and lens rigidity. We also prove a quantitative version of this result uniformly valid in a suitable bounded set of Riemannian metrics. Crucially, we show that Gaussian beam type solutions concentrating on maximal geodesics, split near the boundary into outgoing/incoming parts, such that the phase of the outgoing part contains information on exit point, direction, and travel time. The recovery of lens data then proceeds by a careful stationary phase analysis and a boundary integral identity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01280",
  "author_total": 4,
  "authors": [
    {
      "name": "Mihajlo Cekić"
    },
    {
      "name": "Katya Krupchyk"
    },
    {
      "name": "Suman Kumar Sahoo"
    },
    {
      "name": "Gunther Uhlmann"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3fj91szamfxnj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01280",
  "fulltext_url": null,
  "id": "3fj91szamfxnj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01280",
  "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"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2610|Numerical methods in inverse problems"
    ]
  ],
  "openalex": "W7216019353",
  "pdf_url": "https://arxiv.org/pdf/2610.01280",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3fj91szamfxnj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.01280",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01280"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The anisotropic Calderón problem for Riemannian metrics at high fixed frequency",
  "title_text": "The anisotropic Calderón problem for Riemannian metrics at high fixed frequency",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/3fj91szamfxnj",
  "venue": "arXiv",
  "versions": []
}