Upper semicontinuity of the dimensions of automorphism groups of domains in $C^n$

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

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Upper semicontinuity of the dimensions of automorphism groups of domains in $C^n$

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

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Abstract

Let $H^n$ be the metric space of all bounded domains in $C^n$ 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 $\H^n$. We also provide theorems and examples regarding the change in topological structure of these groups under small perturbation of a domain in $H^n$.

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Buma L. Fridman, Daowei Ma, Evgeny A. Poletsky. 2002-10-18. Upper semicontinuity of the dimensions of automorphism groups of domains in $C^n$. https://arxiv.org/abs/math/0210292

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