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

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

doi:10.1353/ajm.2003.0011

Upper semicontinuity of the dimensions of automorphism groups of domains in ℂ^N

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

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

9 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 language	English (US)
Pages (from-to)	289-299
Number of pages	11
Journal	American Journal of Mathematics
Volume	125
Issue number	2
DOIs	https://doi.org/10.1353/ajm.2003.0011
State	Published - Apr 2003

ASJC Scopus subject areas

General Mathematics

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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.",

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N2 - 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.

AB - 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.

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Upper semicontinuity of the dimensions of automorphism groups of domains in ℂ^N

Abstract

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