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

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

2000-11-02

arxiv.org/abs/math/0011016v1

Mathematics

Differential Geometry

This is the author's 1999 Phd thesis

Scientific paper

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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