{
  "id": "2107.07082",
  "version": "v1",
  "published": "2021-07-15T02:27:01.000Z",
  "updated": "2021-07-15T02:27:01.000Z",
  "title": "Some inequalities on Finsler manifolds with weighted Ricci curvature bounded below",
  "authors": [
    "Xinyue Cheng",
    "Zhongmin Shen"
  ],
  "comment": "21 pages. arXiv admin note: text overlap with arXiv:2009.02632",
  "categories": [
    "math.DG"
  ],
  "abstract": "We establish some important inequalities under a lower weighted Ricci curvature bound on Finsler manifolds. Firstly, we establish a relative volume comparison of Bishop-Gromov type. As one of the applications, we obtain an upper bound for volumes of the Finsler manifolds. Further, when the S-curvature is bounded on the whole manifold, we obtain a theorem of Bonnet-Myers type on Finsler manifolds. Finally, we obtain a sharp Poincar\\'{e}-Lichnerowicz inequality by using integrated Bochner inequality, from which we obtain a sharp lower bound for the first eigenvalue on the Finsler manifolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-15T02:27:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53B40",
      "53C60",
      "58C35"
    ],
    "keywords": [
      "finsler manifolds",
      "inequality",
      "lower weighted ricci curvature bound",
      "sharp lower bound",
      "volume comparison"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}