Inventiones mathematicae

, Volume 180, Issue 3, pp 535–557 | Cite as

Characterizations of lattice surfaces

  • John Smillie
  • Barak WeissEmail author


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.


Lattice Surface Marked Point Quadratic Differential Translation Surface Saddle Connection 
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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Cornell UniversityIthacaUSA
  2. 2.Ben Gurion UniversityBe’er ShevaIsrael

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