{
  "abstract": "We prove that the Dirichlet-to-Neumann map uniquely determines a smooth real Schrödinger potential on any prescribed compact connected smooth Riemannian manifold of dimension at least three with nonempty smooth boundary. The proof combines local continuation of Green kernels with uniform estimates for the associated integral representations on shrinking spheres. These estimates yield local recovery of the potential, and a continuation argument extends this recovery throughout the manifold.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18711",
  "author_total": 4,
  "authors": [
    {
      "name": "Lu Chen"
    },
    {
      "name": "Yan Jiang"
    },
    {
      "name": "Hongyu Liu"
    },
    {
      "name": "Longyue Tao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7zesew6kca55a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18711",
  "fulltext_url": null,
  "id": "7zesew6kca55a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18711",
  "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",
      "2610|Numerical methods in inverse problems"
    ]
  ],
  "openalex": "W7213529480",
  "pdf_url": "https://arxiv.org/pdf/2609.18711",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7zesew6kca55a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2609.18711",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18711"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Determining Schrodinger Potentials on Riemannian Manifolds",
  "title_text": "Determining Schrodinger Potentials on Riemannian Manifolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/7zesew6kca55a",
  "venue": "arXiv",
  "versions": []
}