{
  "id": "1208.0783",
  "version": "v1",
  "published": "2012-08-03T16:03:48.000Z",
  "updated": "2012-08-03T16:03:48.000Z",
  "title": "Some Affine Invariants Revisited",
  "authors": [
    "Alina Stancu"
  ],
  "comment": "15 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We present several sharp inequalities for the SL(n) invariant $\\Omega_{2,n}(K)$ introduced in our earlier work on centro-affine invariants for smooth convex bodies containing the origin. A connection arose with the Paouris-Werner invariant $\\Omega_K$ defined for convex bodies $K$ whose centroid is at the origin. We offer two alternative definitions for $\\Omega_K$ when $K \\in C^2_+$. The technique employed prompts us to conjecture that any SL(n) invariant of convex bodies with continuous and positive centro-affine curvature function can be obtained as a limit of normalized $p$-affine surface areas of the convex body.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-08-03T16:03:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52A40",
      "52A38"
    ],
    "keywords": [
      "convex body",
      "affine surface areas",
      "positive centro-affine curvature function",
      "centro-affine invariants"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.0783S"
    }
  }
}