{
  "id": "2304.11344",
  "version": "v1",
  "published": "2023-04-22T07:52:44.000Z",
  "updated": "2023-04-22T07:52:44.000Z",
  "title": "Results on gradients of harmonic functions on Lipschitz surfaces",
  "authors": [
    "Benjamin Foster"
  ],
  "comment": "18 pages",
  "categories": [
    "math.AP",
    "math.CV"
  ],
  "abstract": "We study various properties of the gradients of solutions to harmonic functions on Lipschitz surfaces. We improve an exponential bound of Naber and Valtorta on the size of the effective critical set to a sharp quadratic bound in this setting using complex analytic tools. We also develop a propagation of smallness for gradients of harmonic functions, settling an open question in this setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-22T07:52:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "harmonic functions",
      "lipschitz surfaces",
      "sharp quadratic bound",
      "complex analytic tools",
      "exponential bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}