Lipschitz Equivalence Of Self-similar Sets

In this paper, we show that all conformal self-similar sets with strong separation condition are quasi-Lipschitz equivalent. we discuss the measure-preserving property of bi-Lipschitz mapping between self-similar sets. As an application, we give an alternative proof of a result of Falconer and Marsh [On the Lipschitz equivalence of Cantor sets, Mathematika,39(1992),223-233], concerning algebraic criteria of bi-Lipschitz equivalence of self-similar sets.