Iwaniec–Martin removability conjecture for bounded quasiregular mappings

Let $E$ be a set in the relevant Euclidean domain, and let $K$-quasiregular mappings be quasiregular mappings with distortion bounded by $K$. A set is removable for bounded $K$-quasiregular mappings if every bounded $K$-quasiregular mapping defined away from the set extends across it as a $K$-quasiregular mapping.

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

$$d = \frac{n}{1+K} \leq \frac{n}{2},$$

are removable under bounded $K$-quasiregular mappings.

This conjecture gives the expected sharp Hausdorff-measure threshold for removability. It is well understood in dimension two in connection with the Painlevé problem, while the higher-dimensional case remains open in the cited context.