Quasiregular mappings and \(d\)-thinness (Q1355888)

\textit{O. Martio} and \textit{J. Sarvas} [Indiana Univ. Math. J. 26, 761-766 (1977; Zbl 0365.30014)] have shown that \(d\)-thinness (or \(d\)-thickness) is invariant under quasiconformal mappings on the \(d\)-dimensional Euclidean space \(\mathbb{R}^d\) \((d\geq 2)\). In this paper, it is shown that the above result holds for quasiregular mappings. A couple of nice applications of the above result is also included.