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

2000/11/02 by Gregory Leibon, Leibon, Gregory · 1 citation
Computer Science · Mathematics · #52C26 #53A30 #60D05 #Computational Geometry and Mesh Generation #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.math/0011016

openalex publication_date 2000/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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