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The ideal Thurston-Andreev theorem and triangulation production

Gregory Leibon
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Abstract

This paper contains a generalization of the convex ideal case of the Thurston-Andreev theorem when the genus is greater than 1. The heart of the paper concerns taking formal angle data on a surface and ``conformally flowing'' this formal angle data to uniquely associated uniform angle data. This flow turns out to be the gradient of an objective function related in a rather magical way to hyperbolic volume.

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Gregory Leibon. 2000-02-17. The ideal Thurston-Andreev theorem and triangulation production. https://arxiv.org/abs/math/0002150

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