Obstructions for automorphic quasiregular maps and Lattès-type uniformly quasiregular maps

Abstract (excerpt)

Suppose that $M$ is a closed, connected, and oriented Riemannian $n$-manifold, $f \colon \mathbb{R}^n \to M$ is a quasiregular map automorphic under a discrete group $Γ$ of Euclidean isometries, and $f$ has finite multiplicity in a fundamental cell of $Γ$. We show that if $Γ$ has a sufficiently large translation subgroup $Γ_T$, then $\dim Γ\in \{0, n-1, n\}$. If $f$ is strongly automorphic and induces a non-injective Lattès-type uniformly quasiregular map, then the same holds without the assumption on the size of $Γ_T$. Moreover, an even stronger restriction holds in the Lattès case if $M$ is

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