A circle packing proof of the Combinatorial Riemann Mapping Theorem

2011/03/11 by Brian Rushton, Rushton, Brian
Computer Science · Materials Science · Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Mathematical Dynamics and Fractals #Quasicrystal Structures and Properties #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1103.2192

openalex publication_date 2011/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The traditional Riemann Mapping Theorem can be proved with circle packing techniques. We prove the Combinatorial Riemann Mapping Theorem for tilings of bounded size using circle packings.

Related

• Convergence of square tilings to the Riemann map
• Computing Circle Packing Representations of Planar Graphs
• Circle packings, renormalizations and subdivision rules
• Circle Packings from Tilings of the Plane
• Combinatorial Space Tiling