7 problems

Quasiregular NILF conjecture. Every such map $f$ has no invariant conformal structure that is non-trivial on its Julia set.

Positive-capacity Julia set conjecture. For every such map,

Boundary equality conjecture. For every quasiregular map of transcendental type,

The conjecture. The conclusions (i)--(v) of Theorem 1 should hold without the hypothesis that $f$ is locally Lipschitz continuous.

Quasiconformal non-conjugacy conjecture. The mappings $h_{K_1,\theta_1}(z)^2+c_1$ and $h_{K_2,\theta_2}(z)^2+c_2$ are not quasiconformally conjugate for every pair…

Let $f:\overline{{\mathbb R}^n}\to\overline{{\mathbb R}^n}$ be quasiregular with $\operatorname{deg}(f)>K_I(f)$. Let $E(f)$ be the exceptional set. A set $X$ is completely invarian…

Lipschitz-free orbit and Julia-set conjecture. The hypothesis that $f$ is Lipschitz continuous can be omitted in Theorems 5 and 7, but not in Theorem 6, which states that…