7 problems

Let $cuOmega\textbackslashsubset\textbackslashmathbb R^n$ be a domain, let $K\textbackslashge 1$, and let $p\textbackslashge 1$. A mapping…

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

Let $U \subset \mathbb R^n$ be open with $n \ge 3$, let $f:U\to f(U)\subset\mathbb R^n$ be a non-constant quasiregular mapping, let $K_I(f)$ denote its inner dilatation, and let…

Let $n\geq 2$, and let $f:\mathbb{R}^n\to\mathbb{R}^n$ be an entire quasiregular Yosida mapping, meaning that the family of translates … is normal. Order conjecture. The order of g…

Sharpness conjecture. There exists a sequence of positive numbers $\epsilon_k\rightarrow 0$ and a sequence of pairs of $Q$-quasiregular maps $u_k:B_1\rightarrow \mathbb{R}^2$,…

A closed set $E\subset \mathbb{R}^n$ is removable under bounded $K$-quasiregular mappings if every bounded $K$-quasiregular mapping defined on an open set minus $E$ extends to a…

Nonvanishing imaginary-part conjecture. Either $\operatorname{Im}(f_z)$ is constant, or