Quasiregular maps of Sierpiński carpet Julia sets

Sergei Merenkov, Letian Shen

We prove that if $f$ and $g$ are postcritically finite rational maps whose Julia sets $\mathcal{J}(f),\mathcal{J}(g)$, respectively, are Sierpiński carpets, and if $\hat{I}¾$ is a quas…