3 papers
math.CA2026
Conformal Dimension of Measures and Quasisymmetric Dimension Reduction
Hua Qiu, Qi Wang
We prove that the conformal dimension of every locally finite Borel measure is either zero or infinite. The main ingredient is a quasisymmetric dimension-reduction theorem: every f…
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…