4 problems

Kneser–Poulsen conjecture for unequal balls. The simultaneous inequalities

Let ${\bf p}=(p_1,\ldots,p_N)$ and ${\bf q}=(q_1,\ldots,q_N)$ be configurations of $N$ points in ${\mathbb E}^d$. The configuration ${\bf q}$ is a contraction of ${\bf p}$ if…

Contraction dual-volume conjecture. Then

Alexander's conjecture. Under arbitrary contraction of the center points of finitely many congruent disks in the Euclidean plane, the perimeter of the intersection of the disks can…