Random Delaunay triangulations, the Thurston-Andreev theorem, and metric uniformization

Gregory Leibon

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arXiv · math/0011016

Random Delaunay triangulations, the Thurston-Andreev theorem, and metric uniformization

Gregory Leibon

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Abstract

In this thesis a connection between the worlds of discrete and continuous conformal geometry is explored. Specifically, a disk pattern production theroem is proved using an energy which measures how ``uniform'' the angle data of a triangulation is, see also math.DG/0002150. Then this energy is averaged over all the Delaunay triangulation of a Riemannian surface to form an energy measuring how ``uniform'' a metric is, see also math.DG/0010316.

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Gregory Leibon. 2000-11-02. Random Delaunay triangulations, the Thurston-Andreev theorem, and metric uniformization. https://arxiv.org/abs/math/0011016

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