5 problems

Let $K\subset\Gamma\times\mathbb{C}^n$, where $\Gamma$ is the boundary of the closed unit disk, and for $z\in\Gamma$ define the fiber … Assume that the fibers $K_z$ are connected a…

Analytic-disc conjecture. The complementary set $\widehat{X}\setminus X$ must contain an analytic disc. This conjecture was disproved by Gabriel Stolzenberg in 1963, who constructe…

Analytic-disc conjecture. Whenever $\widehat{X}\setminus X$ is nonempty, the complementary set

Analytic-disc conjecture. Whenever $\widehat X$ is strictly larger than $X$, the complementary set $\widehat X\setminus X$ must contain an analytic disc.

Let $X$ be a compact set in $\mathbb C^N$, and let $\widehat X$ denote its polynomial hull. The complementary set is $\widehat X\setminus X$. Wermer's analytic-disc conjecture. If…