Domains in \(\mathbb{C}^ n\) with a piecewise Levi flat boundary which possess a noncompact automorphism group (Q811501)

We prove that any bounded convex domain in \(\mathbb{C}^ n\) with a piecewise smooth Levi flat boundary which possesses a noncompact automorphism group is reducible in the sense that it is biholomorphic to a product domain. This, in particular, characterizes the bi-disk in \(\mathbb{C}^ 2\) by its automorphism group.