International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 67, Pages 4229-4239
doi:10.1155/S0161171203303321

Kernel convergence and biholomorphic mappings in several complex variables

Abstract

We deal with kernel convergence of domains in ℂn 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.