Invariants of Bergman geometry and the automorphism groups of domains in \({\mathbb{C}^n}\) (Q2753580)

In the frame of the study of the group of automorphisms \(\Aut (\Omega)\) of a bounded domain \( \Omega\) in \(\mathbb{C}^n\), the authors investigate the type of convexity of a point of accumulation of an orbit of \(\Aut (\Omega)\) . They also show that under certain conditions, the existence of such accumulation points implies that \(\Omega\) is a domain of holomorphy and, under some more general circumstances, diffeomorphic (but certainly not necessarily biholomorphic) to the ball. The behaviour of orbits near an orbit accumulation point is also under investigation here. Finally, they discuss the question of the location of orbits by an invariant involving only two derivatives of the Bergman kernel and deepen the study of this invariant by furnishing some very interesting estimates.NEWLINENEWLINEFor the entire collection see [Zbl 0969.00052].