2 problems

Let $M$ be a manifold with virtually nilpotent fundamental group. Let $\mu(M,g)$ be the minimum number of minimal geodesics such that every other minimal geodesic is asymptotic in…

Let $\operatorname{E}_{\min}(b)$ denote the minimum number of exposed edges among centrally symmetric compact convex polytopes in a real vector space of dimension $b$. A cross-poly…