2 problems

Let $(r_1,\dots,r_k)$ be a sequence of non-negative real numbers satisfying … so that $(r_1,\dots,r_k)$ is convex. Let $T$ be a metric tree with total length…

Let $r>0$, let $T$ be a metric tree with total length $|T|\geq 2r$, and let $\mathcal{C}(T,0)$ denote the relevant space of covers of $T$ by radius-zero centers. Let $E\nu$ denote…