{
  "id": "1803.07787",
  "version": "v1",
  "published": "2018-03-21T08:01:33.000Z",
  "updated": "2018-03-21T08:01:33.000Z",
  "title": "First eigenvalues of geometric operators under the Yamabe flow",
  "authors": [
    "Pak Tung Ho"
  ],
  "comment": "This is the full and detailed version. Accepted by Annals of Global Analysis and Geometry",
  "categories": [
    "math.DG",
    "math.CV"
  ],
  "abstract": "Suppose $(M,g_0)$ is a compact Riemannian manifold without boundary of dimension $n\\geq 3$. Using the Yamabe flow, we obtain estimate for the first nonzero eigenvalue of the Laplacian of $g_0$ with negative scalar curvature in terms of the Yamabe metric in its conformal class. On the other hand, we prove that the first eigenvalue of some geometric operators on a compact Riemannian manifold is nondecreasing along the unnormalized Yamabe flow under suitable curvature assumption. Similar results are obtained for manifolds with boundary and for CR manifold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-21T08:01:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "first eigenvalue",
      "geometric operators",
      "compact riemannian manifold",
      "first nonzero eigenvalue",
      "suitable curvature assumption"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}