The comparability of the Kobayashi approach region and the admissible approach region (Q1104458)

Given \(\Omega \subset \subset {\mathbb{C}}^ n\) a pseudoconvex domain and \(P\in \partial \Omega\) a strongly pseudoconvex point then the admissible approach region \({\mathcal A}_{\alpha}(P)\) of Stein is comparable with the approach region \({\mathfrak K}_{\beta}(P)\) defined in terms of Kobayashi distance. As a result of this we obtain an invariant form of Fatou's theorem on strongly pseudoconvex domains. Also for domains of finite type in \({\mathbb{C}}^ 2\), it is possible to prove that \({\mathfrak K}_{\beta}(P)\) is equivalent to the approach region \({\mathfrak A}_{\sigma}(P)\) defined by balls in the boundary of those domains.