{
  "id": "2311.15524",
  "version": "v1",
  "published": "2023-11-27T03:58:57.000Z",
  "updated": "2023-11-27T03:58:57.000Z",
  "title": "The Ricci iteration towards cscK metrics",
  "authors": [
    "Kewei Zhang"
  ],
  "comment": "Comments are welcome!",
  "categories": [
    "math.DG",
    "math.AP",
    "math.DS"
  ],
  "abstract": "Motivated by the problem of finding constant scalar curvature K\\\"ahler metrics, we investigate a Ricci iteration sequence of Rubinstein that discretizes the pseudo-Calabi flow. While the long time existence of the flow is still an open question, we show that the iteration sequence does exist for all steps, along which the K-energy decreases. We further show that the iteration sequence, modulo automorphisms, converges smoothly to a constant scalar curvature K\\\"ahler metric if there is one, thus confirming a conjecture of Rubinstein from 2007 and extending results of Darvas--Rubinstein to arbitrary K\\\"ahler classes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-27T03:58:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "csck metrics",
      "finding constant scalar curvature",
      "ricci iteration sequence",
      "long time existence",
      "rubinstein"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}