{
  "id": "1806.11235",
  "version": "v1",
  "published": "2018-06-29T00:18:36.000Z",
  "updated": "2018-06-29T00:18:36.000Z",
  "title": "New curvature flows in complex geometry",
  "authors": [
    "Duong H. Phong",
    "Sebastien Picard",
    "Xiangwen Zhang"
  ],
  "comment": "34 pages",
  "categories": [
    "math.DG",
    "math.AP",
    "math.CV"
  ],
  "abstract": "This is a survey of some of the recent developments on the geometric and analytic aspects of the Anomaly flow. It is a flow of $(2,2)$-forms on a $3$-fold which was originally motivated by string theory and the need to preserve the conformally balanced property of a Hermitian metric in the absence of a $\\partial\\bar\\partial$-Lemma. It has revealed itself since to be a remarkable higher order extension of the Ricci flow. It has also led to several other curvature flows which may be interesting from the point of view of both non-K\\\"ahler geometry and the theory of non-linear partial differential equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-29T00:18:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "curvature flows",
      "complex geometry",
      "non-linear partial differential equations",
      "higher order extension",
      "ricci flow"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}