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math.CA2024
The Hausdorff measure and uniform fibre conditions for Barański carpet
Hua Qiu, Qi Wang
For a self-affine carpet of Barański, we establish a dichotomy: $ \text{either }\quad 0<\mathcal{H}^{\dim_{\text{H}} K}(K)<+\infty \quad\text{ or } \quad\mathcal{H}^{\dim_{\tex…
math.CA2024
Assouad and lower dimensions of graph-directed Bedford-McMullen carpets
Hua Qiu, Qi Wang, Shufang Wang
We calculate the Assouad and lower dimensions of graph-directed Bedford-McMullen carpets, which reflect the extreme local scaling laws of the sets, in contrasting with known result…