Configurations in Fractals

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

paper · doi:10.48550/arxiv.2003.09396

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.

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