类型的等价性与 Catlin 边界系
复变函数
2013-08-16 v2 代数几何
摘要
证明了在复 维空间的平滑伪凸域上，D'Angelo 有限类型等价于 Kohn 有限理想类型。这被称为 Kohn 猜想。该论证使用了 Catlin 的边界系概念以及次解析几何和半代数几何的方法。当边界的子集仅包含 Catlin 多类型的两个能级集时，根据 D'Angelo 类型、ambient 空间的维数以及形式的能级，获得了 -Neumann 问题中次椭圆增益的下界。
引用
@article{arxiv.0711.0429,
title = {Equivalence of types and Catlin boundary systems},
author = {Andreea C. Nicoara},
journal= {arXiv preprint arXiv:0711.0429},
year = {2013}
}
备注
Paper withdrawn by the author due to the fact that a Catlin type truncation that is used in the argument may lose finite type, in which case the Levi determinant could be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