Abstract

Let [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="02i" /] be the metric space of all bounded domains in [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="03i" /] with the metric equal to the Hausdorff distance between boundaries of domains. We prove that the dimension of the group of automorphisms of domains is an upper semicontinuous function on [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="04i" /]. We also provide theorems and examples regarding the change in topological structure of these groups under small perturbation of a domain in [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="05i" /].

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 289-299
Launched on MUSE
2003-03-26
Open Access
No
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