{
  "id": "1911.02729",
  "version": "v1",
  "published": "2019-11-07T02:55:58.000Z",
  "updated": "2019-11-07T02:55:58.000Z",
  "title": "Harmonic functions of polynomial growth on gradient shrinking Ricci solitons",
  "authors": [
    "Jia-Yong Wu",
    "Peng Wu"
  ],
  "comment": "29 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "In the previous paper (Math Ann 362:717-742, 2015), we proved that the space of $f$-harmonic functions with polynomial growth on complete non-compact gradient shrinking Ricci soliton $(M, g, f)$ is one-dimensional. In this paper, for a complete non-compact gradient shrinking Ricci soliton of bounded scalar curvature,we prove that the space of harmonic functions with fixed polynomial growth degree is finite dimensional. We also prove analogous results for ancient ($f$-)caloric functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-07T02:55:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C21",
      "35C11",
      "35K05"
    ],
    "keywords": [
      "polynomial growth",
      "harmonic functions",
      "non-compact gradient shrinking ricci soliton",
      "complete non-compact gradient shrinking ricci"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}