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arXiv · 2310.10734

The Residual Set Dimension of a Generalized Apollonian Packing

Daniel Lautzenheiser
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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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Daniel Lautzenheiser. 2023-10-16. The Residual Set Dimension of a Generalized Apollonian Packing. https://arxiv.org/abs/2310.10734

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