{
  "id": "1711.08443",
  "version": "v1",
  "published": "2017-11-22T18:40:26.000Z",
  "updated": "2017-11-22T18:40:26.000Z",
  "title": "Perelman's $W$-functional on manifolds with conical singularities",
  "authors": [
    "Xianzhe Dai",
    "Changliang Wang"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper, we develop the theory of Perelman's $W$-functional on manifolds with isolated conical singularities. In particular, we show that the infimum of $W$-functional over a certain weighted Sobolev space on manifolds with isolated conical singularities is finite, and the minimizer exists, if the scalar curvature satisfies certain condition near the singularities. We also obtain an asymptotic order for the minimizer near the singularities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-22T18:40:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "functional",
      "isolated conical singularities",
      "scalar curvature satisfies",
      "asymptotic order",
      "weighted sobolev space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}