Jun Luo (Chongqing University):  

Lipschitz equivalence of self-similar fractals

Abstract: The talk will introduce the progress on the Lipschitz equivalence of self-similar sets which has been a hot topic in fractal geometry. First we define an augmented tree on fractals, we show that the augmented tree is a Gromov hyperbolic graph and its hyperbolic boundary can be identified with the self-similar set. Then by using this connection we provide a complete Lipschitz classification of integral self-similar sets under the open set condition. Some generalizations will also be involved.