Circle packing coordinates for the moduli space of tori

Williams, G.

doi:10.1090/S0002-9939-2010-10690-1

Circle packing coordinates for the moduli space of tori
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by G. Brock Williams PDF

Proc. Amer. Math. Soc. 139 (2011), 2577-2585 Request permission

Abstract:

We develop a set of natural coordinates $(\alpha ,\beta )$ on the moduli space of Euclidean tori using the combinatorial structure of circle packings. Surfaces with rational coordinates support Brooks packings, while surfaces with rational $\alpha$ and irrational $\beta$ coordinates support generalized Brooks packings with periodic singularities.

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