{
  "id": "1404.0878",
  "version": "v1",
  "published": "2014-04-03T12:28:22.000Z",
  "updated": "2014-04-03T12:28:22.000Z",
  "title": "Stable foliations with respect to Fuglede modulus and level sets of $p$--harmonic functions",
  "authors": [
    "Malgorzata Ciska--Niedzialomska",
    "Kamil Niedzialomski"
  ],
  "comment": "16 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "We continue the study of the variation of the $p$--modulus of a foliation initiated by the first author. We derive the formula for the second variation which allows to study $p$--stable foliations. We obtain some results concerning codimension one $p$--stable foliations. Moreover, we derive the equation for the critical point of the $p$--modulus functional of a foliation given by the level sets of smooth function. We show the correlation with the $q$--harmonicity. We give some examples. In particular, we show that foliations given by the distance function are critical points of $p$--modulus functional.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-03T12:28:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58E35",
      "58E20",
      "53C12"
    ],
    "keywords": [
      "stable foliations",
      "level sets",
      "fuglede modulus",
      "harmonic functions",
      "modulus functional"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.0878C"
    }
  }
}