{
  "id": "1111.0278",
  "version": "v1",
  "published": "2011-11-01T19:20:33.000Z",
  "updated": "2011-11-01T19:20:33.000Z",
  "title": "Quasi-potentials and regularization of currents, and applications",
  "authors": [
    "Tuyen Trung Truong"
  ],
  "comment": "11 pages",
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "Let $Y$ be a compact K\\\"ahler manifold. We show that the weak regularization $K_n$ of Dinh and Sibony for the diagonal $\\Delta_Y$ (see Section 2 for more detail) is compatible with wedge product in the following sense: If $T$ is a positive $dd^c$-closed $(p,p)$ current and $\\theta$ is a smooth $(q,q)$ form then there is a sequence of positive $dd^c$-closed $(p+q,p+q)$ currents $S_n$ whose masses converge to 0 so that $-S_n\\leq K_n(T\\wedge \\theta)-K_n(T)\\wedge \\theta \\leq S_n$ for all $n$. We also prove a result concerning the quasi-potentials of positive closed currents. We give two applications of these results. First, we prove a corresponding compatibility with wedge product for the pullback operator defined in our previous paper. Second, we define an intersection product for positive $dd^c$-closed currents. This intersection is symmetric and has a local nature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-11-01T19:20:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F99",
      "32H50"
    ],
    "keywords": [
      "applications",
      "quasi-potentials",
      "wedge product",
      "closed currents",
      "weak regularization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.0278T"
    }
  }
}