2 papers
math.CA2025
From Lipschitz embedding to Lipschitz equivalence between dust-like self-similar sets
Huo-Jun Ruan, Jian-Ci Xiao
Let be two dust-like self-similar sets sharing the same Hausdorff dimension. We consider when the mere existence of a Lipschitz embedding from to a…
math.GN2025
The connectedness of SierpiÅski sponges with rotational and reflectional components and associated graph-directed systems
Huo-Jun Ruan, Jian-Ci Xiao
We provide two methods to characterize the connectedness of all -dimensional generalized SierpiÅski sponges whose corresponding IFSs are allowed to have rotational and reflecti…