Abstract
We calculate the area of the smallest triangle and the area of the smallest virtual triangle for many known lattice surfaces. We show that our list of the lattice surfaces for which the area of the smallest virtual triangle greater than \(1\over 20\) is complete. In particular, this means that there are no new lattice surfaces for which the area of the smallest virtual triangle is greater than .05. Our method follows an algorithm described by Smillie and Weiss and improves on it in certain respects.
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Acknowledgments
The author thanks his thesis advisor John Smillie for suggesting the problem and for many helpful conversations, and Alex Wright and Anja Randecker for many helpful comments.
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Wu, C. Lattice surfaces and smallest triangles. Geom Dedicata 187, 107–121 (2017). https://doi.org/10.1007/s10711-016-0191-z
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DOI: https://doi.org/10.1007/s10711-016-0191-z