{
  "id": "2107.03599",
  "version": "v1",
  "published": "2021-07-08T04:26:40.000Z",
  "updated": "2021-07-08T04:26:40.000Z",
  "title": "A Liouville theorem for the Neumann problem of the Monge-Ampere equation",
  "authors": [
    "Huaiyu Jian",
    "Xushan Tu"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we study the Neumann problem of Monge-Amp\\`ere equations in Semi-space. For two dimensional case, we prove that its viscosity convex solutions must be a quadratic polynomial. When the space dimension $n\\geq 3$, we show that the conclusion still holds if either the boundary value is zero or the viscosity convex solutions restricted on some $n-2$ dimensional subspace is bounded from above by a quadratic function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-08T04:26:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "neumann problem",
      "monge-ampere equation",
      "liouville theorem",
      "viscosity convex solutions",
      "dimensional case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}