{
  "id": "1811.01646",
  "version": "v1",
  "published": "2018-11-05T12:48:30.000Z",
  "updated": "2018-11-05T12:48:30.000Z",
  "title": "On existence of the prescribing $k$-curvature of the Einstein tensor",
  "authors": [
    "Leyang Bo",
    "Weimin Sheng"
  ],
  "comment": "14 pages. All comments are welcome",
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper, we study the problem of conformally deforming a metric on a $3$-dimensional manifold $M^3$ such that its $k$-curvature equals to a prescribed function, where the $k$-curvature is defined by the $k$-th elementary symmetric function of the eigenvalues of the Einstein tensor, $1\\le k\\le 3$. We prove the solvability of the problem and the compactness of the solution sets on manifolds when $k=2$ and $3$, provided the conformal class admits a negative $k$-admissible metric with respect to the Einstein tensor.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-05T12:48:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C21",
      "35J60"
    ],
    "keywords": [
      "einstein tensor",
      "th elementary symmetric function",
      "conformal class admits",
      "prescribing",
      "dimensional manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}