{
  "id": "1807.00928",
  "version": "v1",
  "published": "2018-07-02T23:46:30.000Z",
  "updated": "2018-07-02T23:46:30.000Z",
  "title": "Tian's properness conjectures: an introduction to Kahler geometry",
  "authors": [
    "Yanir A. Rubinstein"
  ],
  "categories": [
    "math.DG",
    "math.AP",
    "math.CV"
  ],
  "abstract": "This manuscript served as lecture notes for a mini-course in the 2016 Southern California Geometric Analysis Seminar Winter School. The goal is to give a quick introduction to Kahler geometry by describing the recent resolution of Tian's three influential properness conjectures in joint work with T. Darvas. These results---inspired by and analogous to work on the Yamabe problem in conformal geometry---give an analytic characterization for the existence of Kahler--Einstein metrics and other important canonical metrics in complex geometry, as well as strong borderline Sobolev type inequalities referred to as the (strong) Moser--Trudinger inequalities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-02T23:46:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32Q20",
      "58E11",
      "53C25",
      "53C55",
      "14J50",
      "32W20",
      "32U05"
    ],
    "keywords": [
      "tians properness conjectures",
      "kahler geometry",
      "california geometric analysis seminar",
      "strong borderline sobolev type inequalities",
      "geometric analysis seminar winter school"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}