Based on some ideas of Greene and Krantz, we study#R##N#the semicontinuity of automorphism groups of domains in one#R##N#and several complex variables. We show that semicontinuity fails#R##N#for domains in , , with Lipschitz boundary, but it holds#R##N#for domains in  with Lipschitz boundary. Using the same ideas, we develop some other concepts related to mappings of Lipschitz#R##N#domains. These include Bergman curvature, stability properties#R##N#for the Bergman kernel, and also some ideas about equivariant#R##N#embeddings.
['Steven G. Krantz']
Semicontinuity of the Automorphism Groups of Domains with Rough Boundary