Equivalence of types and Catlin boundary systems

Details Equivalence of types and Catlin boundary systems Equivalence of types and Catlin boundary systems

2007-11-03

arxiv.org/abs/0711.0429v1

Mathematics

Complex Variables

52 pages; a simpler proof of the Kohn Conjecture

Scientific paper

The D'Angelo finite type is shown to be equivalent to the Kohn finite ideal type on smooth, pseudoconvex domains in complex n space. This is known as the Kohn Conjecture. The argument uses Catlin's notion of a boundary system as well as methods from subanalytic and semialgebraic geometry. When a subset of the boundary contains only two level sets of the Catlin multitype, a lower bound for the subelliptic gain in the \bar\partial-Neumann problem is obtained in terms of the D'Angelo type, the dimension of the ambient space, and the level of forms.

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