English

Characterizations of lattice surfaces

Dynamical Systems 2008-09-23 v1

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.

Keywords

Cite

@article{arxiv.0809.3729,
  title  = {Characterizations of lattice surfaces},
  author = {John Smillie and Barak Weiss},
  journal= {arXiv preprint arXiv:0809.3729},
  year   = {2008}
}
R2 v1 2026-06-21T11:22:51.066Z