{
  "id": "1805.07701",
  "version": "v1",
  "published": "2018-05-20T04:04:43.000Z",
  "updated": "2018-05-20T04:04:43.000Z",
  "title": "Energy-minimizing maps from manifolds with nonnegative Ricci curvature",
  "authors": [
    "James Dibble"
  ],
  "comment": "15 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "The energy of any $C^1$ representative of a homotopy class of maps from a compact and connected Riemannian manifold with nonnegative Ricci curvature into a complete Riemannian manifold with no conjugate points is bounded below by the energy of a totally geodesic surjection onto a flat semi-Finsler manifold, with equality if and only if the original map is totally geodesic. This conclusion also holds under the weaker assumption that the domain is finitely covered by a diffeomorphic product, and its universal covering space splits isometrically as a product with a flat factor, in a commutative diagram that follows from the Cheeger-Gromoll splitting theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-20T04:04:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C21",
      "53C24",
      "53C22",
      "53C45"
    ],
    "keywords": [
      "nonnegative ricci curvature",
      "energy-minimizing maps",
      "complete riemannian manifold",
      "totally geodesic",
      "universal covering space splits"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}