I need to show that Riemann Mapping Theorem is not true in general for $\mathbb{C^n}$. I know Cartan's Uniqueness Theorem and $Aut(B)$ acts transitively on $B$.
But I am unable to deduce the result
Thanks for the help!!
2025-01-13 03:01:42.1736737302
Riemann Mapping theorem doesn't hold true in Several Complex Variables
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The automorphism of the bi-disk is $PSU(1,1)^2 \times Z/2Z$, the automorphism of the ball is $PSU(2,1)$. These groups are not the same. In fact if you just know $Aut(B)$, it is enough to check that $PSU(1,1)^2 \subset Aut(B_1^2)$ do not embed in $PSU(2,1)= Aut(B_2)$.