{
  "id": "2404.01040",
  "version": "v2",
  "published": "2024-04-01T10:50:57.000Z",
  "updated": "2024-06-01T05:14:31.000Z",
  "title": "Monge-Ampère equations with right-hand sides of polynomial growth",
  "authors": [
    "Beomjun Choi",
    "Kyeongsu Choi",
    "Soojung Kim"
  ],
  "comment": "A part of this work was introduced in arXiv:2104.13186v1; however, we have separated and further elaborated the result to accommodate issues that will be dealt in the revision of arXiv:2104.13186. In v2, we generalized the main theorems slightly so that they apply for broader class of equations",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "We study the regularity and the growth rates of solutions to two-dimensional Monge-Amp\\`ere equations with the right-hand side exhibiting polynomial growth. Utilizing this analysis, we demonstrate that the translators for the flow by sub-affine-critical powers of the Gauss curvature are smooth, strictly convex entire graphs. These graphs exhibit specific growth rates that depend solely on the power of the flow.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-06-01T05:14:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53E99",
      "35J96"
    ],
    "keywords": [
      "monge-ampère equations",
      "right-hand side exhibiting polynomial growth",
      "specific growth rates",
      "strictly convex entire graphs",
      "gauss curvature"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}