LAUSR

The quasi-Lipschitz mappings, weaker than the bi-Lipschitz mappings, preserve Hausdorff, packing and box dimensions, but change Assouad dimension dimA(⋅). In this paper, for Moran fractals, we investigate the change of their Assouad dimension under the quasi-Lipschitz mappings. We study a class of Moran set which is quasi-Lipschitz Assouad-minimal, i.e. for any E in the class, dimAf(E) ≥dimA(E) for all quasi-Lipschitz mappings f defined on E. For another class of Moran sets, we prove that for any F in the class, infgdimAg(F) =dimqAF, where the infimum is taken over all quasi-Lipschitz mappings g defined on F, and dimqA(⋅) is the quasi-Assouad dimension introduced in [F. Lu and L. F. Xi, Quasi-Assouad dimension of fractals, J. Fractal Geom. 3 (2016) 187–215].