{
  "id": "2108.08402",
  "version": "v1",
  "published": "2021-08-18T22:12:25.000Z",
  "updated": "2021-08-18T22:12:25.000Z",
  "title": "A Green's function proof of the Positive Mass Theorem",
  "authors": [
    "V. Agostiniani",
    "L. Mazzieri",
    "F. Oronzio"
  ],
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "In this short note, a new proof of the Positive Mass Theorem is established through a newly discovered monotonicity formula, holding along the level sets of the Green's function of an asymptotically flat $3$-manifolds. In the same context and for $1<p<3$, a Geroch-type calculation is performed along the level sets of $p$-harmonic functions, leading to a new proof of the Riemannian Penrose Inequality in some case studies.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-18T22:12:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C21",
      "31C12",
      "31C15",
      "53C24",
      "53Z05"
    ],
    "keywords": [
      "positive mass theorem",
      "greens function proof",
      "level sets",
      "riemannian penrose inequality",
      "geroch-type calculation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}