3 problems

Regularity conjecture. The unit sphere of $d_\infty$ is rectifiable with respect to every Riemannian distance on $G_\infty$. In particular, if $G_\infty$ has topological dimension…

Let $G$ be a simply connected nilpotent Lie group, let $\Gamma$ be a discrete co-compact subgroup, and let $S$ be a finite symmetric generating set containing the identity. Let…

Let $G$ be a simply connected nilpotent Lie group and let $\Gamma$ be a discrete co-compact subgroup. For a finite symmetric generating set $S\subset\Gamma$, let $\rho_S$ be the as…