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The Residual Set Dimension of a Generalized Apollonian Packing

2023/10/16 by Lautzenheiser, Daniel
#FOS: Mathematics #Metric Geometry (math.MG) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2310.10734

Abstract

We view space-filling circle packings as subsets of the boundary of hyperbolic space subject to symmetry conditions based on a discrete group of isometries. This allows for the application of counting methods which admit rigorous upper and lower bounds on the Hausdorff dimension of the residual set of a generalized Apollonian circle packing. This dimension (which also coincides with a critical exponent) is strictly greater than that of the Apollonian packing.

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