{
  "id": "2001.07406",
  "version": "v1",
  "published": "2020-01-21T09:35:04.000Z",
  "updated": "2020-01-21T09:35:04.000Z",
  "title": "Stability of line bundle mean curvature flow",
  "authors": [
    "Xiaoli Han",
    "Xishen Jin"
  ],
  "comment": "All comments are welcome!",
  "categories": [
    "math.DG"
  ],
  "abstract": "Let $(X,\\omega)$ be a compact K\\\"ahler manifold of complex dimension $n$ and $(L,h)$ be a holomorphic line bundle over $X$. The line bundle mean curvature flow was introduced in \\cite{JY} in order to find deformed Hermitian-Yang-Mills metrics on $L$. In this paper, we consider the stability of the line bundle mean curvature flow. Suppose there exists a deformed Hermitian Yang-Mills metric $\\hat h$ on $L$. We prove that the line bundle mean curvature flow converges to $\\hat h$ exponentially in $C^\\infty$ sense as long as the initial metric is close to $\\hat h$ in $C^2$-norm.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-21T09:35:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "line bundle mean curvature flow",
      "bundle mean curvature flow converges",
      "deformed hermitian yang-mills metric",
      "holomorphic line bundle",
      "initial metric"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}