3 problems

Let $a<b$ be coprime positive integers, and let … For a finite set $S\subset\mathbb{Z}$, write $d_p(S)$ for its packing density and $d_c(S)$ for its covering density. The packing a…

Let $p$ range over $1<p<\infty$, and consider the curve whose value at $p$ is the maximum covering constant for the Minkowski ball $D_p$. The curve of maxima conjecture. The curve…

Let $d\geqslant 2$ be fixed. For a $d$-dimensional convex body $C$, let $\delta(C)$ and $\theta(C)$ denote its packing and covering densities by congruent copies. Kuperberg's conje…