The Residual Set Dimension of a Generalized Apollonian Packing
Number Theory
2023-10-18 v1 Metric Geometry
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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Cite
@article{arxiv.2310.10734,
title = {The Residual Set Dimension of a Generalized Apollonian Packing},
author = {Daniel Lautzenheiser},
journal= {arXiv preprint arXiv:2310.10734},
year = {2023}
}
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14 pages