{
  "id": "2410.20563",
  "version": "v1",
  "published": "2024-10-27T19:32:28.000Z",
  "updated": "2024-10-27T19:32:28.000Z",
  "title": "Concentration of eigenfunctions on singular Riemannian manifolds",
  "authors": [
    "Charlotte Dietze",
    "Larry Read"
  ],
  "comment": "11 pages",
  "categories": [
    "math.AP",
    "astro-ph.EP",
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "We consider a compact Riemannian manifold with boundary and a metric that is singular at the boundary. The associated Laplace-Beltrami operator is of the form of a Grushin operator plus a singular potential. In a supercritical parameter regime, we identify the rate of concentration and profile of the high-frequency eigenfunctions that accumulate at the boundary. We give an application to acoustic modes on gas planets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-27T19:32:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58C40",
      "53C17",
      "35P20"
    ],
    "keywords": [
      "singular riemannian manifolds",
      "concentration",
      "compact riemannian manifold",
      "grushin operator plus",
      "singular potential"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}