{
  "id": "1710.02037",
  "version": "v1",
  "published": "2017-10-05T14:18:23.000Z",
  "updated": "2017-10-05T14:18:23.000Z",
  "title": "The Dirichlet Problem for Einstein Metrics on Cohomogeneity One Manifolds",
  "authors": [
    "Timothy Buttsworth"
  ],
  "comment": "16 pages, no figures",
  "categories": [
    "math.DG"
  ],
  "abstract": "Let $G/H$ be a compact homogeneous space, and let $\\hat{g}_0$ and $\\hat{g}_1$ be $G$-invariant Riemannian metrics on $G/H$. We consider the problem of finding a $G$-invariant Einstein metric $g$ on the manifold $G/H\\times [0,1]$ subject to the constraint that $g$ restricted to $G/H\\times \\{0\\}$ and $G/H\\times \\{1\\}$ coincides with $\\hat{g}_0$ and $\\hat{g}_1$, respectively. By assuming that the isotropy representation of $G/H$ consists of pairwise inequivalent irreducible summands, we show that we can always find such an Einstein metric.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-05T14:18:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C20",
      "53C30",
      "58J32"
    ],
    "keywords": [
      "dirichlet problem",
      "cohomogeneity",
      "invariant einstein metric",
      "invariant riemannian metrics",
      "compact homogeneous space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}