Semicontinuity of the Automorphism Groups of Domains with Rough Boundary
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 d...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2012/934295 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |