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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65352Let $H^n$ 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 pagesComplex Variables32M05; 54H15Upper semicontinuity of the dimensions of automorphism groups of domains in $C^n$text