{
  "id": "2310.14943",
  "version": "v1",
  "published": "2023-10-23T13:41:31.000Z",
  "updated": "2023-10-23T13:41:31.000Z",
  "title": "Gradient Bounds and Liouville theorems for Quasi-linear equations on compact Manifolds with nonnegative Ricci curvature",
  "authors": [
    "Dimitrios Gazoulis",
    "George Zacharopoulos"
  ],
  "comment": "12 pages",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "In this work we establish a gradient bound and Liouville-type theorems for solutions to Quasi-linear elliptic equations on compact Riemannian Manifolds with nonnegative Ricci curvature. Also, we provide a local slitting theorem when the inequality in the gradient bound becomes equality at some point. Moreover, we prove a Harnack-type inequality and an ABP estimate for the gradient of solutions in domains contained in the manifold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-23T13:41:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J05",
      "35J62",
      "53C24"
    ],
    "keywords": [
      "nonnegative ricci curvature",
      "gradient bound",
      "liouville theorems",
      "quasi-linear equations",
      "compact manifolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}