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arXiv · 0711.0429

Equivalence of types and Catlin boundary systems

Andreea C. Nicoara
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Abstract

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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Andreea C. Nicoara. 2013-08-15. Equivalence of types and Catlin boundary systems. https://arxiv.org/abs/0711.0429

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