Finite trees inside thin subsets of ${\mathbb{R}}^d$

Abstract

Bennett, Iosevich and Taylor proved that compact subsets of ${\mathbb{R}}^d$, $d\ge 2$, of Hausdorff dimensions greater than $\frac{d+1}{2}$ contain chains of arbitrary length with gaps in a non-trivial interval. In this paper we generalize this result to arbitrary tree configurations.

References in corpus (1)

• Equilateral triangles in subsets of ${\mathbb{R}}^d$ of large Hausdorff dimension