{
  "id": "1408.1115",
  "version": "v2",
  "published": "2014-08-05T21:10:28.000Z",
  "updated": "2014-09-12T17:04:15.000Z",
  "title": "The Euler characteristic of a surface from its Fourier analysis in one direction",
  "authors": [
    "Nguyen Viet Dang"
  ],
  "comment": "Section 3 entirely rewritten, appendix made shorter, formula (8) in Theorem 2.1 for $\\chi(S)$ in the older version had wrong sign now corrected, new results related to the Radon transform added",
  "categories": [
    "math.GT",
    "math.AP"
  ],
  "abstract": "In this paper, we prove that we can recover the genus of a closed compact surface $S$ in $\\mathbb{R}^3$ from the restriction to a generic line of the Fourier transform of the canonical measure carried by $S$. We also show that the restriction on some line in Minkowski space of the solution of a linear wave equation whose Cauchy data comes from the canonical measure carried by $S$, allows to recover the Euler characteristic of $S$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-05T21:10:28.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-09-12T17:04:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A27",
      "35A18",
      "57R70"
    ],
    "keywords": [
      "euler characteristic",
      "fourier analysis",
      "cauchy data comes",
      "linear wave equation",
      "canonical measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}