{
  "id": "2208.00298",
  "version": "v1",
  "published": "2022-07-30T19:46:37.000Z",
  "updated": "2022-07-30T19:46:37.000Z",
  "title": "Stability of determination of Riemann surface from its DN-map in terms of Teichmüller distance",
  "authors": [
    "M. I. Belishev",
    "D. V. Korikov"
  ],
  "comment": "25 pages, 0 figures",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "As is known, the Dirichlet-to-Neumann operator $\\Lambda$ of a Riemannian surface $(M,g)$ determines the surface up to conformal equivalence class $[(M,g)]$. Such classes constitute the Teichm\\\"uller space with the distance ${\\rm d}_T$. We show that the determination is continuous: $\\|\\Lambda-\\Lambda'\\|_{H^1(\\partial M)\\to L_2(\\partial M)}\\to 0$ implies ${\\rm d}_T([(M,g)],[(M',g')])\\to 0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-30T19:46:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R30",
      "46J15",
      "46J20",
      "30F15"
    ],
    "keywords": [
      "riemann surface",
      "teichmüller distance",
      "determination",
      "conformal equivalence class",
      "dirichlet-to-neumann operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}