International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 67, Pages 4229-4239

Kernel convergence and biholomorphic mappings in several complex variables

Gabriela Kohr

Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 1 M. Kogălniceanu Street, Cluj-Napoca 3400, Romania

Received 27 March 2003

Copyright © 2003 Gabriela Kohr. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We deal with kernel convergence of domains in 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.