{
  "id": "0809.3729",
  "version": "v1",
  "published": "2008-09-22T15:48:09.000Z",
  "updated": "2008-09-22T15:48:09.000Z",
  "title": "Characterizations of lattice surfaces",
  "authors": [
    "John Smillie",
    "Barak Weiss"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We answer a question of Vorobets by showing that the lattice property for flat surfaces is equivalent to the existence of a positive lower bound for the areas of affine triangles. We show that the set of affine equivalence classes of lattice surfaces with a fixed positive lower bound for the areas of triangles is finite and we obtain explicit bounds on its cardinality. We deduce several other characterizations of the lattice property.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-09-22T15:48:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lattice surfaces",
      "characterizations",
      "lattice property",
      "affine equivalence classes",
      "affine triangles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.3729S"
    }
  }
}