{
  "id": "1811.04204",
  "version": "v1",
  "published": "2018-11-10T06:49:47.000Z",
  "updated": "2018-11-10T06:49:47.000Z",
  "title": "On the Gradient of Harmonic Functions",
  "authors": [
    "Pisheng Ding"
  ],
  "categories": [
    "math.CA",
    "math.AP",
    "math.DG"
  ],
  "abstract": "For a harmonic function u on Euclidean space, this note shows that |grad(u)| is essentially determined by the geometry of level hypersurfaces of u. Specifically, the factor by which |grad(u)| changes along a gradient flow is completely determined by the mean curvature of the level hypersurfaces intersecting the flow.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-10T06:49:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31B05"
    ],
    "keywords": [
      "harmonic function",
      "euclidean space",
      "gradient flow",
      "mean curvature"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}