{
  "id": "1610.07829",
  "version": "v1",
  "published": "2016-10-25T11:16:43.000Z",
  "updated": "2016-10-25T11:16:43.000Z",
  "title": "Regularity of Harmonic Maps from Polyhedra to CAT(1) Spaces",
  "authors": [
    "Christine Breiner",
    "Ailana Fraser",
    "Lan-Hsuan Huang",
    "Chikako Mese",
    "Pam Sargent",
    "Yingying Zhang"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "We determine regularity results for energy minimizing maps from an $n$-dimensional Riemannian polyhedral complex $X$ into a CAT(1) space. Provided that the metric on $X$ is Lipschitz regular, we prove H\\\"older regularity with H\\\"older constant and exponent dependent on the total energy of the map and the metric on the domain. Moreover, at points away from the $(n-2)$-skeleton, we improve the regularity to locally Lipschitz. Finally, for points $x \\in X^{(k)}$ with $k \\leq n-2$, we demonstrate that the H\\\"older exponent depends on geometric and combinatorial data of the link of $x \\in X$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-25T11:16:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C43"
    ],
    "keywords": [
      "harmonic maps",
      "dimensional riemannian polyhedral complex",
      "determine regularity results",
      "lipschitz regular",
      "energy minimizing maps"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}