{
  "id": "2304.06323",
  "version": "v1",
  "published": "2023-04-13T08:04:49.000Z",
  "updated": "2023-04-13T08:04:49.000Z",
  "title": "Extremizers of the $J$ functional with respect to the $d_1$ metric",
  "authors": [
    "Sam Bachhuber",
    "Aaron Benda",
    "Benjamin Christophel",
    "Tamás Darvas"
  ],
  "comment": "Results from an REU project. arXiv admin note: text overlap with arXiv:2101.02589",
  "journal": "Analysis Math. 48 (2022), no. 2, 307-330",
  "categories": [
    "math.DG",
    "math.CV"
  ],
  "abstract": "In previous work, Darvas-George-Smith obtained inequalities between the large scale asymptotic of the $J$ functional with respect to the $d_1$ metric on the space of toric K\\\"ahler metrics/rays. In this work we prove sharpness of these inequalities on all toric K\\\"ahler manifolds, and study the extremizing potentials/rays. On general K\\\"ahler manifolds we show that existence of radial extremizers is equivalent with the existence of plurisupported currents, as introduced and studied by McCleerey.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-13T08:04:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "functional",
      "large scale asymptotic",
      "radial extremizers",
      "inequalities",
      "metrics/rays"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}