{
  "id": "2006.08451",
  "version": "v1",
  "published": "2020-06-15T14:55:58.000Z",
  "updated": "2020-06-15T14:55:58.000Z",
  "title": "Symmetry and Isoperimetry for Riemannian Surfaces",
  "authors": [
    "Joseph Ansel Hoisington",
    "Peter McGrath"
  ],
  "comment": "Comments welcome!",
  "categories": [
    "math.DG",
    "math.AP",
    "math.CA"
  ],
  "abstract": "For a domain $\\Omega$ in a geodesically convex surface, we introduce a scattering energy $\\mathcal{E}(\\Omega)$, which measures the asymmetry of $\\Omega$ by quantifying its incompatibility with an isometric circle action. We prove several sharp quantitative isoperimetric inequalities involving $\\mathcal{E}(\\Omega)$ and characterize the domains with vanishing scattering energy by their convexity and rotational symmetry.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-15T14:55:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C45",
      "53C65",
      "53C24"
    ],
    "keywords": [
      "riemannian surfaces",
      "isoperimetry",
      "scattering energy",
      "sharp quantitative isoperimetric inequalities",
      "isometric circle action"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}