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.
Cite
@article{arxiv.0809.3729,
title = {Characterizations of lattice surfaces},
author = {John Smillie and Barak Weiss},
journal= {arXiv preprint arXiv:0809.3729},
year = {2008}
}