{
  "id": "1403.5552",
  "version": "v2",
  "published": "2014-03-21T19:38:29.000Z",
  "updated": "2014-08-07T19:32:36.000Z",
  "title": "Boundedness of Laplacian eigenfunctions on manifolds of infinite volume",
  "authors": [
    "Leonardo Bonorino",
    "Patrícia Klaser",
    "Miriam Telichevesky"
  ],
  "comment": "13 pages; change in the title; change in the abstract; improvement in the introduction; added some details in the proof of Theorem 2.2",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "In a Hadamard manifold $M$, it is proved that if $u$ is a $\\lambda$-eigenfunction of the Laplacian that belongs to $L^p(M)$ for some $p \\ge 2$, then $u$ is bounded and $\\|u\\|_{\\infty} \\le C \\|u\\|_p,$ where $C$ depends only on $p$, $\\lambda$ and on the dimension of $M$. This result is obtained in the more general context of a complete Riemannian manifold endowed with an isoperimetric function $H$ satisfying some integrability condition. In this case, the constant $C$ depends on $p,\\lambda$ and $H.$",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-08-07T19:32:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J50",
      "58J05"
    ],
    "keywords": [
      "infinite volume",
      "laplacian eigenfunctions",
      "boundedness",
      "general context",
      "hadamard manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.5552B"
    }
  }
}