{
  "id": "2409.14151",
  "version": "v1",
  "published": "2024-09-21T14:08:35.000Z",
  "updated": "2024-09-21T14:08:35.000Z",
  "title": "Numerical calculation method for function integration on submanifolds of $\\mathbb{R}^n$ or compact Riemannian manifolds",
  "authors": [
    "Fusheng Deng",
    "Gang Huang",
    "Yingyi Wu"
  ],
  "categories": [
    "math.NA",
    "cs.NA",
    "math.DG"
  ],
  "abstract": "In this paper, we present a method for digitally representing the \"volume element\" and calculating the integral of a function on compact hypersurfaces with or without boundary, and low-dimensional submanifolds in $\\mathbb{R}^n$. We also extend such calculation to hypersurfaces in compact Riemannnian manifolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-21T14:08:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "compact riemannian manifolds",
      "numerical calculation method",
      "function integration",
      "compact riemannnian manifolds",
      "volume element"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}