{
  "id": "math/0311460",
  "version": "v1",
  "published": "2003-11-26T00:07:58.000Z",
  "updated": "2003-11-26T00:07:58.000Z",
  "title": "Some estimates related to Oh's conjecture for the Clifford tori in CP^n",
  "authors": [
    "Edward Goldstein"
  ],
  "categories": [
    "math.DG",
    "math.SG"
  ],
  "abstract": "This note is motivated by Y.G. Oh's conjecture that the Clifford torus $L_n$ in $\\mathbb{C}P^n$ minimizes volume in its Hamiltonian deformation class. We show that there exist explicit positive constants $a_n$ depending on the dimension with $a_2=3/\\pi$ such that for any Lagrangian torus $L$ in the Hamiltonian class of $L_n$ we have $vol(L) \\geq a_n vol (L_n)$. The proof uses the recent work of C.H. Cho on Floer homology of the Clifford tori. A formula from integral geometry enables us to derive the estimate. We wish to point out that a general lower bound on the volume of $L$ exists from the work of C. Viterbo. Our lower bound $a_2= 3/\\pi$ is the best one we know.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-11-26T00:07:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "clifford torus",
      "ohs conjecture",
      "hamiltonian deformation class",
      "general lower bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....11460G"
    }
  }
}