{
  "id": "1404.3234",
  "version": "v2",
  "published": "2014-04-11T21:57:23.000Z",
  "updated": "2014-09-28T17:44:34.000Z",
  "title": "Equivalence of optimal $L^1$-inequalities on Riemannian Manifolds",
  "authors": [
    "Jurandir Ceccon",
    "Leandro Cioletti"
  ],
  "comment": "To appear in Journal of Mathematical Analysis and Its Applications (JMAA)",
  "doi": "10.1016/j.jmaa.2014.09.041",
  "categories": [
    "math.AP"
  ],
  "abstract": "Let $(M,g)$ be a smooth compact Riemannian manifold of dimension $n \\geq 2$. This paper concerns to the validity of the optimal Riemannian $L^1$-Entropy inequality \\[ {\\bf Ent}_{dv_g}(u) \\leq n \\log \\left(A_{opt} \\|D u\\|_{BV(M)} + B_{opt}\\right) \\] for all $u \\in BV(M)$ with $\\|u\\|_{L^1(M)} = 1$ and existence of extremal functions. In particular, we prove that this optimal inequality is equivalent a optimal $L^1$-Sobolev inequality obtained by Druet [6].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-11T21:57:23.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-09-28T17:44:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "equivalence",
      "smooth compact riemannian manifold",
      "paper concerns",
      "optimal riemannian",
      "entropy inequality"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.3234C"
    }
  }
}