Holomorphic automorphisms of certain class of domains of infinite type (Q1338411)

This paper investigates the holomorphic automorphisms of a special kind of Hartogs' domains in \(\mathbb{C}^ 2\): \[ E_ p = \bigl\{ (z_ 1, z_ 2) \in \mathbb{C}^ 2 : | z_ 1 |^ 2 + P(z_ 1, \overline z_ 2) < 1 \bigr\} \] where \(P\) is a subharmonic function with \(P(0) = 0\). These automorphisms form a group \(\Aut (E_ p)\), and its compactness is proved, if \(D\) is of infinite type, which means, at any point of the boundary \(\partial D\), the Levi form for \(D\) vanishes up to the infinite order in the complex tangential direction.