
doi: 10.2307/1971087
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.
boundary invariant, existence of subelliptic estimates for the \({\bar \partial }\)-Neumann problem, multitype of boundary points, Pseudoconvex domains, \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs, \(\overline\partial\) and \(\overline\partial\)-Neumann operators, smoothly bounded pseudoconvex domain
boundary invariant, existence of subelliptic estimates for the \({\bar \partial }\)-Neumann problem, multitype of boundary points, Pseudoconvex domains, \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs, \(\overline\partial\) and \(\overline\partial\)-Neumann operators, smoothly bounded pseudoconvex domain
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