A Rudin's theorem for model domains
OURIMI, Nabil . 2021
For any ${\mathcal C}^{\infty}$-smooth almost complex structure $J'$ on ${\mathbb C}^{n+1},$ we prove that any proper holomorphic mapping from a model domain in ${\mathbb C}^{n+1}$ to a bounded domain in $({\mathbb C}^{n+1}, J')$, that has a ${\mathcal C}^1$-extension to the boundary is factored by a finite group of automorphisms $\Gamma $, conjugate to a finite subgroup of $Id_{\mathbb C}\times U(n)$. Further, we obtain rigidity results when additional conditions are imposed on the target domain. Our main result extends Rudin's theorem, on proper holomorphic mappings and finite reflection groups, to the almost complex case.
For any ${\mathcal C}^{\infty}$-smooth almost complex structure $J'$ on ${\mathbb C}^{n+1},$ we prove that any proper holomorphic mapping from a model domain in ${\mathbb C}^{n+1}$ to a bounded…
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