{
  "id": "1310.6326",
  "version": "v2",
  "published": "2013-10-23T18:49:20.000Z",
  "updated": "2013-11-03T17:04:14.000Z",
  "title": "Hermitian metrics, (n-1, n-1) forms and Monge-Ampère equations",
  "authors": [
    "Valentino Tosatti",
    "Ben Weinkove"
  ],
  "comment": "37 pages, v2 some corrections to computations in Section 3",
  "categories": [
    "math.DG",
    "math.CV"
  ],
  "abstract": "We show existence of unique smooth solutions to the Monge-Ampere equation for (n-1)-plurisubharmonic functions on Hermitian manifolds, generalizing previous work of the authors. As a consequence we obtain Calabi-Yau theorems for Gauduchon and strongly Gauduchon metrics on a class of non-Kahler manifolds: those satisfying the Jost-Yau condition known as Astheno-Kahler. Gauduchon conjectured in 1984 that a Calabi-Yau theorem for Gauduchon metrics holds on all compact complex manifolds. We discuss another Monge-Ampere equation, recently introduced by Popovici, and show that the full Gauduchon conjecture can be reduced to a second order estimate of Hou-Ma-Wu type.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-11-03T17:04:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32U05",
      "32W20",
      "32Q15",
      "53C55"
    ],
    "keywords": [
      "monge-ampère equations",
      "hermitian metrics",
      "monge-ampere equation",
      "calabi-yau theorem",
      "full gauduchon conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.6326T"
    }
  }
}