3 problems

Generalized Sierpinski carpet criticality conjecture. For generalized Sierpinski carpets and similar fractals,

Let $G$ be a hyperbolic group, and let $S$ be the Sierpiński carpet. Let $\partial G$ denote the boundary of $G$, and let $\mathbb{H}^3$ denote hyperbolic 3-space. Kapovich–Kleiner…

Let a generalized Sierpinski carpet have self-similar, possibly graph-directed, structures yielding the same Laplacian operator. Let $d_k$ denote the relevant dimensions, with…