Characterizations of lattice surfaces

John Smillie; Barak Weiss

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arXiv · 0809.3729

Characterizations of lattice surfaces

John Smillie·Barak Weiss

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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.

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John Smillie, Barak Weiss. 2008-09-22. Characterizations of lattice surfaces. https://arxiv.org/abs/0809.3729

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