Boundary invariants of pseudoconvex domains. (English) Zbl 0583.32048

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.
Reviewer: St.Krantz


32T99 Pseudoconvex domains
32W05 \(\overline\partial\) and \(\overline\partial\)-Neumann operators
35N15 \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs
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