{
  "id": "1707.03660",
  "version": "v1",
  "published": "2017-07-12T12:01:51.000Z",
  "updated": "2017-07-12T12:01:51.000Z",
  "title": "$C^{1,1}$ regularity for degenerate complex Monge-Ampère equations and geodesic rays",
  "authors": [
    "Jianchun Chu",
    "Valentino Tosatti",
    "Ben Weinkove"
  ],
  "comment": "22 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "We prove a $C^{1,1}$ estimate for solutions of complex Monge-Amp\\`ere equations on compact K\\\"ahler manifolds with possibly nonempty boundary, in a degenerate cohomology class. This strengthens previous estimates of Phong-Sturm. As applications we deduce the local $C^{1,1}$ regularity of geodesic rays in the space of K\\\"ahler metrics associated to a test configuration, as well as the local $C^{1,1}$ regularity of quasi-psh envelopes in nef and big classes away from the non-K\\\"ahler locus.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-12T12:01:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J96",
      "32Q15",
      "32W20",
      "53C55"
    ],
    "keywords": [
      "degenerate complex monge-ampère equations",
      "geodesic rays",
      "regularity",
      "big classes away",
      "degenerate cohomology class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}