{
  "id": "1904.02391",
  "version": "v1",
  "published": "2019-04-04T07:43:19.000Z",
  "updated": "2019-04-04T07:43:19.000Z",
  "title": "An $\\varepsilon$-regularity theorem for line bundle mean curvature flow",
  "authors": [
    "Xiaoli Han",
    "Hikaru Yamamoto"
  ],
  "comment": "41 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper, we study the line bundle mean curvature flow defined by Jacob and Yau. The line bundle mean curvature flow is a kind of parabolic flows to obtain deformed Hermitian Yang-Mills metrics on a given K\\\"ahler manifold. The goal of this paper is to give an $\\varepsilon$-regularity theorem for the line bundle mean curvature flow. To establish the theorem, we provide a scale invariant monotone quantity. As a critical point of this quantity, we define self-shrinker solution of the line bundle mean curvature flow. The Liouville type theorem for self-shrinkers is also given. It plays an important role in the proof of the $\\varepsilon$-regularity theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-04T07:43:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "line bundle mean curvature flow",
      "regularity theorem",
      "scale invariant monotone quantity",
      "deformed hermitian yang-mills metrics",
      "define self-shrinker solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}