663 research outputs found
Direct Proof of Termination of the Kohn Algorithm in the Real-Analytic Case
In 1979 J.J. Kohn gave an indirect argument via the Diederich-Forn\ae ss
Theorem showing that finite D'Angelo type implies termination of the Kohn
algorithm for a pseudoconvex domain with real-analytic boundary. We give here a
direct argument for this same implication using the stratification coming from
Catlin's notion of a boundary system as well as algebraic geometry on the ring
of real-analytic functions. We also indicate how this argument could be used in
order to compute an effective lower bound for the subelliptic gain in the
-Neumann problem in terms of the D'Angelo type, the dimension of
the space, and the level of forms provided that an effective \L ojasiewicz
inequality can be proven in the real-analytic case and slightly more
information obtained about the behavior of the sheaves of multipliers in the
Kohn algorithm.Comment: 33 page
On the Relationship between D'Angelo q-type and Catlin q-type
We establish inequalities relating two measurements of the order of contact
of q-dimensional complex varieties with a real hypersurface.Comment: 18 pages; accepted at the Journal of Geometric Analysis; see
arXiv:1102.0356 for the origin of this investigatio
Relating Catlin and D'Angelo -types
We clarify the relationship between the two most standard measurements of the
order of contact of q-dimensional complex varieties with a real hypersurface,
the Catlin and D'Angelo -types, by showing that the former equals the
generic value of the normalized order of contact measured along curves whose
infimum is by definition the D'Angelo -type.Comment: 11 pages. arXiv admin note: text overlap with arXiv:1302.229
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