3 problems

Let $K=\{p_1,p_2,\dots,p_n\}$ be a finite set in a normed plane $\mathbb{M}^2$, and let $\lambda\geq\lambda_K$. A minimal-arc representation conjecture asserts that there exist bal…

Perturbation conjecture. For every $\epsilon>0$, there is a set $S'=\{p'_1,p'_2,\ldots,p'_n\}$ in bijective correspondence with $S$ such that each corresponding pair satisfies…

Let $K=\{p_1,p_2,\dots,p_n\}$ be a finite set in a normed plane $\mathbb{M}^2$, and let $\lambda\geq\lambda_K$. The ball intersection $\operatorname{bi}(K,\lambda)$ and the ball hu…