2008/09/22 by John Smillie, Smillie, John, Barak Weiss +1 · 1 citation
Materials Science · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Quasicrystal Structures and Properties
paper · pdf · doi:10.48550/arxiv.0809.3729
openalex publication_date 2008/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.