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

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

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

Authors

Fridman, Buma L.

Ma, Daowei

Poletsky, Evgeny A.

Description

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 $H^n$.
11 pages