{
  "id": "1306.5079",
  "version": "v1",
  "published": "2013-06-21T09:20:56.000Z",
  "updated": "2013-06-21T09:20:56.000Z",
  "title": "Comparison Theorems for Manifold with Mean Convex Boundary",
  "authors": [
    "Jian Ge"
  ],
  "comment": "13pages. submitted",
  "categories": [
    "math.DG"
  ],
  "abstract": "Let $M^n$ be an $n$-dimensional Riemannian manifold with boundary $\\partial M$. Assume that Ricci curvature is bounded from below by $(n-1)k$, for $k\\in \\RR$, we give a sharp estimate of the upper bound of $\\rho(x)=\\dis(x, \\partial M)$, in terms of the mean curvature bound of the boundary. When $\\partial M$ is compact, the upper bound is achieved if and only if $M$ is isometric to a disk in space form. A Kaehler version of estimation is also proved. Moreover we prove a Laplace comparison theorem for distance function to the boundary of Kaehler manifold and also estimate the first eigenvalue of the real Laplacian.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-06-21T09:20:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mean convex boundary",
      "upper bound",
      "mean curvature bound",
      "laplace comparison theorem",
      "dimensional riemannian manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.5079G"
    }
  }
}