Lipschitz equivalence of self-similar sets and hyperbolic boundaries. II. (Q2344487)

This paper is a continuation of earlier work by \textit{J. J. Luo} and \textit{K.-S. Lau} [Adv. Math. 235, 555--579 (2013; Zbl 1267.28011)] on the study of Lipschitz equivalences. A major assumption in the main theorem of the above publication is now removed using the new notion of a quasi-rearrangeable matrix. Additionally, it is shown that the hyperbolic boundary of any simple augmented tree is Lipschitz equivalent to a Cantor-type set. Based on this result, the Lipschitz equivalence of certain totally disconnected self-similar sets as well as their unions is considered.