2 problems

Let $n>1$, let $N<2n-1$, and let $f$ be a proper holomorphic mapping from the unit ball … into … which is $C^2$-smooth up to the boundary. Cima–Suffridge conjecture. There exist au…

Let $A,B,C,D$ be four non-overlapping unit balls in $\mathbb{R}^3$. A geometric permutation is the order in which a line transversal meets the balls. Incompatibility conjecture. Th…