{
  "id": "1901.11263",
  "version": "v1",
  "published": "2019-01-31T08:33:35.000Z",
  "updated": "2019-01-31T08:33:35.000Z",
  "title": "Axially symmetric solutions of Allen-Cahn equation with finite Morse index",
  "authors": [
    "Changfeng Gui",
    "Kelei Wang",
    "Juncheng Wei"
  ],
  "comment": "19 pages; comments are welcome",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we study axially symmetric solutions of Allen-Cahn equation with finite Morse index. It is shown that there does not exist such a solution in dimensions between $4$ and $10$. In dimension $3$, we prove that these solutions have finitely many ends. Furthermore, the solution has exactly two ends if its Morse index equals $1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-31T08:33:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite morse index",
      "allen-cahn equation",
      "study axially symmetric solutions",
      "morse index equals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}