{
  "id": "2008.13282",
  "version": "v1",
  "published": "2020-08-30T21:34:33.000Z",
  "updated": "2020-08-30T21:34:33.000Z",
  "title": "Gradient and Eigenvalue Estimates on the canonical bundle of Kähler manifolds",
  "authors": [
    "Zhiqin Lu",
    "Qi S. Zhang",
    "Meng Zhu"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "We prove certain gradient and eigenvalue estimates, as well as the heat kernel estimates, for the Hodge Laplacian on $(m,0)$ forms, i.e., sections of the canonical bundle of K\\\"ahler manifolds, where $m$ is the complex dimension of the manifold. Instead of the usual dependence on curvature tensor, our condition depends only on the Ricci curvature bound. The proof is based on a new Bochner type formula for the gradient of $(m, 0)$ forms, which involves only the Ricci curvature and the gradient of the scalar curvature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-30T21:34:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58A10",
      "58J35",
      "58J50"
    ],
    "keywords": [
      "eigenvalue estimates",
      "canonical bundle",
      "kähler manifolds",
      "heat kernel estimates",
      "bochner type formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}