{
  "id": "1405.0401",
  "version": "v2",
  "published": "2014-05-02T13:43:24.000Z",
  "updated": "2014-12-02T18:39:50.000Z",
  "title": "Convexity of the K-energy on the space of Kahler metrics and uniqueness of extremal metrics",
  "authors": [
    "Robert J. Berman",
    "Bo Berndtsson"
  ],
  "comment": "v1: 26 pages, v2: 31 pages (improved exposition and a new title)",
  "categories": [
    "math.DG",
    "math.CV"
  ],
  "abstract": "We establish the convexity of Mabuchi's K-energy functional along weak geodesics in the space of Kahler potentials on a compact Kahler manifold thus confirming a conjecture of Chen and give some applications in Kahler geometry, including a proof of the uniqueness of constant scalar curvature metrics (or more generally extremal metrics) modulo automorphisms. The key ingredient is a new local positivity property of weak solutions to the homogenuous Monge-Ampere equation on a product domain, whose proof uses local Bergman kernels.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-02T13:43:24.000Z",
      "title": "Convexity of the K-energy on the space of Kähler metrics",
      "comment": "26 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-12-02T18:39:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "kähler metrics",
      "constant scalar curvature metrics",
      "mabuchis k-energy functional",
      "compact kahler manifold",
      "local positivity property"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.0401B"
    }
  }
}