{
  "id": "2401.03394",
  "version": "v1",
  "published": "2024-01-07T05:46:40.000Z",
  "updated": "2024-01-07T05:46:40.000Z",
  "title": "Liouville theorem for minimal graphs over manifolds of nonnegative Ricci curvature",
  "authors": [
    "Qi Ding"
  ],
  "comment": "14 pages",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "Let $\\Sigma$ be a complete Riemannian manifold of nonnegative Ricci curvature. We prove a Liouville-type theorem: every smooth solution $u$ to minimal hypersurface equation on $\\Sigma$ is a constant provided $u$ has sublinear growth for its negative part. Here, the sublinear growth condition is sharp. Our proof relies on a gradient estimate for minimal graphs over $\\Sigma$ with small linear growth of the negative parts of graphic functions via iteration.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-07T05:46:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonnegative ricci curvature",
      "minimal graphs",
      "liouville theorem",
      "small linear growth",
      "minimal hypersurface equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}