2007/11/03 by Andreea C. Nicoara, Nicoara, Andreea C. · 2 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Geometric and Algebraic Topology #Holomorphic and Operator Theory #math.AG #math.CV #msc:32W05
paper · pdf · doi:10.48550/arxiv.0711.0429
Paper withdrawn by the author due to the fact that a Catlin type truncation that is used in the argument may lose finite type, in which case the Levi determinant could be identically zero in the domain of the truncation. An example of this kind and the proof that the Levi determinant only vanishes to an effective order for smooth domains of finite type appears in arXiv:1102.0356
arxiv created 2013/08/15 · arxiv updated 2013/08/16
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 ∂-Neumann problem is obtained in terms of the D'Angelo type, the dimension of the ambient space, and the level of forms.