Characterizations of lattice surfaces

John Smillie, Barak Weiss*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)535-557
Number of pages23
JournalInventiones Mathematicae
Issue number3
StatePublished - Jun 2010
Externally publishedYes


FundersFunder number
Directorate for Mathematical and Physical Sciences0302357


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