5 problems

Vitushkin's conjecture. The set $E$ is non-removable for bounded holomorphic functions if and only if its orthogonal projections have positive length in a set of directions of posi…

Iwaniec–Martin removability conjecture. Sets of Hausdorff $d$-measure zero, where

Rigidity–removability conjecture. Rigidity of a circle domain is equivalent to $\operatorname{QCH}$-removability of its boundary.

A connected open set $\Omega$ in the Riemann sphere $\widehat{\mathbb C}$ is a circle domain if each boundary component of $\Omega$ is either a circle or a point. It is rigid if ev…

Let $s>0$, $\beta\geq 0$, $p>1$, and let $K\subset\mathbb R^N$ be compact. Denote by $\operatorname{cap}^{\mathbb R^N}_{\frac{2s(1+\beta)}{p},p'}(K)$ the corresponding Bessel capac…