{
  "abstract": "We prove uniqueness for an inverse boundary problem for the prescribed Gaussian curvature equation $\\det D^2u=K(x)(1+|\\nabla u|^2)^2$ on a smooth bounded simply connected planar domain. We compare smooth positive curvatures on a common open class of Dirichlet values for which the convex problems are well posed. Equality of the nonlinear Dirichlet-to-Neumann maps, together with the prescribed first boundary jet of the curvature, implies equality of the curvatures throughout the domain. The first linearized equation has conductivity $Σ=K(D^2u)^{-1}$. The planar anisotropic conductivity theorem determines this tensor up to a boundary fixing diffeomorphism. We prove that the Hessian and gradient structure forces this diffeomorphism to be the identity. The difference between the pulled-back background gradient and the original gradient satisfies a local elliptic system whose components have the same scalar principal part and zero boundary Cauchy data. A first-order Carleman estimate gives unique continuation for this system. The argument uses the nonlinear boundary response at one admissible Dirichlet value and its first derivative there.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.04657",
  "author_total": 1,
  "authors": [
    {
      "name": "Yi-Hsuan Lin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/178s26vef2v9d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.04657",
  "fulltext_url": null,
  "id": "178s26vef2v9d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.04657",
  "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": "W7167588331",
  "pdf_url": "https://arxiv.org/pdf/2607.04657",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/178s26vef2v9d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2607.04657",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.04657"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Gauge rigidity in an inverse problem for the prescribed Gaussian curvature equation",
  "title_text": "Gauge rigidity in an inverse problem for the prescribed Gaussian curvature equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/178s26vef2v9d",
  "venue": "arXiv",
  "versions": []
}