Upper semicontinuity of the dimensions of automorphism groups of domains in ℂN

Buma L. Fridman, Daowei Ma, Evgeny A. Poletsky

Research output: Contribution to journalArticle

7 Scopus citations

Abstract

Let ℋn be the metric space of all bounded domains in ℂn 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 ℋn. We also provide theorems and examples regarding the change in topological structure of these groups under small perturbation of a domain ℋn.

Original languageEnglish (US)
Pages (from-to)289-299
Number of pages11
JournalAmerican Journal of Mathematics
Volume125
Issue number2
StatePublished - Apr 1 2003

ASJC Scopus subject areas

  • Mathematics(all)

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