5 problems

Let $q\geq 2$ be an integer, let $n\geq 3-2^{1-q}$, and for points $x_1,\ldots,x_n\in\mathbb{R}^q$ let $S(x_1,\ldots,x_n)$ be the smallest $(q-1)$-dimensional sphere enclosing them…

Let $q\geq 2$ be an integer. For points $x_1,\ldots,x_n\in\mathbb{R}^q$, let $S(x_1,\ldots,x_n)$ be the smallest $(q-1)$-dimensional sphere enclosing them, and let…

Let $q\geq 2$ be an integer, and let $d\colon(\mathbb{R}^q)^n\to\mathbb{R}$ assign to $(x_1,\ldots,x_n)$ the number of distinct lines determined by the points. Let $K_n^*$ be its a…

For each $n$, let $K_n^*$ denote the associated best constant of the circle-based $n$-distance considered in the paper. Asymptotic constant conjecture. … The paper proves the lower…

Let $q\geq 1$ and let $d\colon(\mathbb{R}^q)^n\to\mathbb{R}_+$ assign to $(x_1,\ldots,x_n)$ the total length of a minimal spanning tree of the complete Euclidean graph on these poi…