Configurations in Fractals

2020/03/20 by Nikolaos Chatzikonstantinou, Chatzikonstantinou, Nikolaos
Mathematics · #28A75 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:28A75

paper · pdf · doi:10.48550/arxiv.2003.09396

arxiv created 2020/03/20 · arxiv updated 2020/03/23

Abstract

We define the manifold of configurations to be the quotient set of k points in Euclidean space identified under congruence, and prove that compact subsets of ℝ^d, d ≥ 2, of large Hausdorff dimension have a non-null set of configurations in them. Our method simplifies previous work in arXiv:1708.05919 and achieves a better dimensional threshold.

Citations

• Rigidity, graphs and Hausdorff dimension

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