Boundary invariants of pseudoconvex domains
Let \(\Omega \subseteq {\mathbb{C}}^ n\) be a smoothly bounded pseudoconvex domain. A notion of multitype of a point \(P\in \partial \Omega\) is introduced. This term is defined in terms of directional derivatives of a defining function for \(\partial \Omega\). The principal theorem of this paper demonstrates the naturality of the notion of multitype. In particular, the concept of multitype is compared to an algebro-geometric notion which was introduced previously by D'Angelo. In a later paper (to appear) Catlin proves that his notion of finite multitype is equivalent with the existence of subelliptic estimates for the \({\bar \partial}\)-Neumann problem.
existence of subelliptic estimates for the \({\bar \partial }\)-Neumann problem
scientific article; zbMATH DE number 3933470