{
  "id": "1708.03937",
  "version": "v1",
  "published": "2017-08-13T17:30:11.000Z",
  "updated": "2017-08-13T17:30:11.000Z",
  "title": "Perelman's $λ$-functional on manifolds with conical singularities",
  "authors": [
    "Xianzhe Dai",
    "Changliang Wang"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper, we prove that on a compact manifold with isolated conical singularity the spectrum of the Schr\\\"odinger operator $-4\\Delta+R$ consists of discrete eigenvalues with finite multiplicities, if the scalar curvature $R$ satisfies a certain condition near the singularity. Moreover, we obtain an asymptotic behavior for eigenfunctions near the singularity. As a consequence of these spectral properties, we extend the theory of the Perelman's $\\lambda$-functional on smooth compact manifolds to compact manifolds with isolated conical singularities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-13T17:30:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "functional",
      "isolated conical singularity",
      "smooth compact manifolds",
      "discrete eigenvalues",
      "finite multiplicities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}