Convergence of square tilings to the Riemann map

2019/10/15 by Agelos Georgakopoulos, Christoforos Panagiotis, Georgakopoulos, Agelos +1
Mathematics · #05C10 #30C35 #60J10 #Analytic and geometric function theory #Combinatorics (math.CO) #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Dynamics and Fractals #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1910.06886

openalex publication_date 2019/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A well-known theorem of Rodin & Sullivan, previously conjectured by Thurston, states that the circle packing of the intersection of a lattice with a simply connected planar domain Ω into the unit disc \mathbbD converges to a Riemann map from Ω to \mathbbD when the mesh size converges to 0. We prove the analogous statement when circle packings are replaced by the square tilings of Brooks et al.

Citations

• �ber die partiellen Differenzengleichungen der mathematischen Physik

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