{
  "id": "1008.4311",
  "version": "v1",
  "published": "2010-08-25T16:31:39.000Z",
  "updated": "2010-08-25T16:31:39.000Z",
  "title": "The gradient flow of the $L^2$ curvature energy on surfaces",
  "authors": [
    "Jeffrey Streets"
  ],
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "We investigate the gradient flow of the $L^2$ norm of the Riemannian curvature on surfaces. We show long time existence with arbitrary initial data, and exponential convergence of the volume normalized flow to a constant scalar curvature metric when the initial energy is below a constant determined by the Euler characteristic of the underlying surface.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-08-25T16:31:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gradient flow",
      "curvature energy",
      "constant scalar curvature metric",
      "long time existence",
      "arbitrary initial data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1008.4311S"
    }
  }
}