Kernel convergence and biholomorphic mappings in several complex variables (Q1774353)

Summary: We deal with kernel convergence of domains in \(\mathbb{C}^n\) which are biholomorphically equivalent to the unit ball \(B\). We also prove that there is an equivalence between the convergence on compact sets of biholomorphic mappings on \(B\), which satisfy a growth theorem, and the kernel convergence. Moreover, we obtain certain consequences of this equivalence in the study of Loewner chains and of starlike and convex mappings on \(B\).