{
  "id": "2108.04761",
  "version": "v1",
  "published": "2021-08-10T15:55:29.000Z",
  "updated": "2021-08-10T15:55:29.000Z",
  "title": "Hessian estimates for the conjugate heat equation coupled with the Ricci flow",
  "authors": [
    "Hong Huang"
  ],
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "In this note we obtain local and global Hessian estimates for the conjugate heat equation coupled with the Ricci flow. As an application, we extend Perelman's monotonicity formula of the $W$-entropy to the noncompact situation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-10T15:55:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conjugate heat equation",
      "ricci flow",
      "extend perelmans monotonicity formula",
      "global hessian estimates",
      "noncompact situation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}