{
  "id": "1609.08849",
  "version": "v1",
  "published": "2016-09-28T10:12:57.000Z",
  "updated": "2016-09-28T10:12:57.000Z",
  "title": "Volume comparison with respect to scalar curvature",
  "authors": [
    "Wei Yuan"
  ],
  "comment": "25 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "In this article, we investigate the volume comparison with respect to scalar curvature. In particular, we show volume comparison hold for small geodesic balls of metrics near $V$-static metrics. As for global results, we give volume comparison for metrics near Einstein metrics with certain restrictions. As an application, we recover a volume comparison result of compact hyperbolic manifolds due to Besson-Courtois-Gallot, which provides a partial answer to a conjecture of Schoen on volume of hyperbolic manifolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-28T10:12:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C20",
      "58J37",
      "53C23",
      "53C24"
    ],
    "keywords": [
      "scalar curvature",
      "volume comparison hold",
      "volume comparison result",
      "compact hyperbolic manifolds",
      "small geodesic balls"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}