{
  "id": "1003.1707",
  "version": "v1",
  "published": "2010-03-08T20:13:34.000Z",
  "updated": "2010-03-08T20:13:34.000Z",
  "title": "The gradient flow of the $L^2$ curvature energy near the round sphere",
  "authors": [
    "Jeff Streets"
  ],
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "We investigate the low-energy behavior of the gradient flow of the $L^2$ norm of the Riemannian curvature on four-manifolds. Specifically, we show long time existence and exponential convergence to a metric of constant sectional curvature when the initial metric has positive Yamabe constant and small initial energy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-03-08T20:13:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gradient flow",
      "round sphere",
      "curvature energy",
      "small initial energy",
      "long time existence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1003.1707S"
    }
  }
}