Configurations in Fractals

Nikolaos Chatzikonstantinou

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arXiv · 2003.09396

Configurations in Fractals

Nikolaos Chatzikonstantinou

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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 $\mathbb{R}^d, d \geq 2$, 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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BibTeX RIS

Nikolaos Chatzikonstantinou. 2020-03-20. Configurations in Fractals. https://arxiv.org/abs/2003.09396

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