On the boundary orbit accumulation set for a domain with non-compact automorphism group

摘要

For a smoothly bounded pseudoconvex domain $D\subset{\Bbb C}^n$ of finitetype with non-compact holomorphic automorphism group $\text{Aut}(D)$, we showthat the set $S(D)$ of all boundary accumulation points for $\text{Aut}(D)$ isa compact subset of $\partial D$ and, if $S(D)$ contains at least three points,it is connected and thus has the power of the continuum. We also discuss how$S(D)$ relates to other invariant subsets of $\partial D$ and show inparticular that $S(D)$ is always a subset of the \v{S}ilov boundary.