{
  "id": "0807.4213",
  "version": "v1",
  "published": "2008-07-26T04:11:45.000Z",
  "updated": "2008-07-26T04:11:45.000Z",
  "title": "Matzoh ball soup in spaces of constant curvature",
  "authors": [
    "Genqian Liu"
  ],
  "comment": "28 pages",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "In this paper, we generalize Magnanini-Sakaguchi's result [MS3] from Euclidean space to spaces of constant curvature. More precisely, we show that if a conductor satisfying the exterior geodesic sphere condition in the space of constant curvature has initial temperature 0 and its boundary is kept at temperature 1 (at all times), if the thermal conductivity of the conductor is inverse of its metric, and if the conductor contains a proper sub-domain, satisfying the interior geodesic cone condition and having constant boundary temperature at each given time, then the conductor must be a geodesic ball. Moreover, we show similar result for the wave equations and the Schr\\\"{o}dinger equations in spaces of constant curvature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-07-26T04:11:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K05",
      "35K20",
      "35J05",
      "58J35",
      "35J10"
    ],
    "keywords": [
      "constant curvature",
      "matzoh ball soup",
      "exterior geodesic sphere condition",
      "interior geodesic cone condition",
      "constant boundary temperature"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0807.4213L"
    }
  }
}