S. Eriksson-Bique

On universal elements for doubling geodesic trees

For $n\ge 3$ and $c\in(0,1)$, let $\mathcal{GT}(n,c)$ denote the class of geodesic metric trees of valence at most $n$ whose branch points are uniformly relatively separated with constant $c$. We prove that $\mathcal{GT}(n,c)$ has no bi-Lipschitz universal element. More precisely, we construct a family $(T_a)_{a\in[1/4...