Simplices in thin subsets of Euclidean spaces

Abstract

Let $\De$ be a non-degenerate simplex on $k$ vertices. We prove that there exists a threshold $s_k<k$ such that any set $A\subs \R^k$ of Hausdorff dimension $dimA\ge s_k$ necessarily contains a similar copy of the simplex $\De$.

arXiv admin note: text overlap with arXiv:2006.15723

Cited by in corpus (2)

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