From Lipschitz embedding to Lipschitz equivalence between dust-like self-similar sets

Huo-Jun Ruan, Jian-Ci Xiao

Let $K,F\subset {\mathbb{R}}^d$ be two dust-like self-similar sets sharing the same Hausdorff dimension. We consider when the mere existence of a Lipschitz embedding from $K$ to $F$ a…