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Annals of Mathematics
Article . 1984 . Peer-reviewed
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Boundary Invariants of Pseudoconvex Domains

Boundary invariants of pseudoconvex domains
Authors: Catlin, David;

Boundary Invariants of Pseudoconvex Domains

Abstract

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.

Keywords

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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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
106
Top 10%
Top 1%
Top 10%
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