{
  "abstract": "We establish an $L^p$--$L^q$-type Carleman estimate for the Schrödinger operator $H_{A,V}$ with scaling-critical electromagnetic singular potentials on a conical singular space $(X,g)$ of dimension $d\\geq3$, where the metric is $g=dr^2+r^2h$ and $X=C(Y)=(0,\\infty)_r\\times Y$ is a product cone over the closed Riemannian manifold $(Y,h)$. More precisely, we prove $$ \\|e^{τϕ}u\\|_{L^{2d/(d-2)}(X)}\\le C\\,\\|e^{τϕ}H_{A,V}u\\|_{L^{2d/(d+2)}(X)} $$ with the quadratic weight $ϕ(r)=\\tfrac14(\\log r)^2$, uniformly in $τ$. As an application of this Carleman estimate, we prove the unique continuation property for this electromagnetic Schrödinger operator when the cross-section is $Y=\\mathbb{S}^{d-1}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09721",
  "author_total": 3,
  "authors": [
    {
      "name": "Baiyang Yin"
    },
    {
      "name": "Fang Zhang"
    },
    {
      "name": "Junyong Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/609pj2shmx0eq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09721",
  "fulltext_url": null,
  "id": "609pj2shmx0eq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09721",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.09721",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/609pj2shmx0eq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.09721",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09721"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Carleman Estimates for Critical Electromagnetic Schrödinger Operators on Conic Manifolds",
  "title_text": "Carleman Estimates for Critical Electromagnetic Schrödinger Operators on Conic Manifolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/609pj2shmx0eq",
  "venue": "arXiv",
  "versions": []
}