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International Journal of Mathematics and Mathematical Sciences
Volume 2012, Article ID 934295, 7 pages
Research Article

Semicontinuity of the Automorphism Groups of Domains with Rough Boundary

Department of Mathematics, Washington University in St. Louis, St. Louis, MO 63130, USA

Received 14 August 2012; Accepted 15 October 2012

Academic Editor: Palle E. Jorgensen

Copyright © 2012 Steven G. Krantz. 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.


Based on some ideas of Greene and Krantz, we study the semicontinuity of automorphism groups of domains in one and several complex variables. We show that semicontinuity fails for domains in , , with Lipschitz boundary, but it holds for domains in with Lipschitz boundary. Using the same ideas, we develop some other concepts related to mappings of Lipschitz domains. These include Bergman curvature, stability properties for the Bergman kernel, and also some ideas about equivariant embeddings.