{
  "id": "2208.03504",
  "version": "v1",
  "published": "2022-08-06T12:09:36.000Z",
  "updated": "2022-08-06T12:09:36.000Z",
  "title": "On the parabolic Donaldson's equation over a compact complex manifold",
  "authors": [
    "Liangdi Zhang"
  ],
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "We prove the uniqueness and long time existence of the smooth solution to a parabolic Donaldson's equation on a compact complex manifold $M$.Then we show that a suitably normalized solution converges to a smooth function on $M$ in $C^\\infty$ topology as $t\\rightarrow\\infty$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-06T12:09:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C55",
      "35K10",
      "35B45",
      "58J35"
    ],
    "keywords": [
      "compact complex manifold",
      "parabolic donaldsons equation",
      "long time existence",
      "smooth solution",
      "suitably normalized solution converges"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}