The core of the Levi distribution

Levi核的修正

Modifications of the Levi core

该研究构造了以含Levi零分布的闭分布为指标的修正Levi核族，建立了其与Catlin性质(P)的等价刻画，证明了二维复空间中修正Levi核的重合性及满足性质(P)的完全Hartogs域上修正Levi核的平凡性，深化了Levi核相关理论。

关于Levi核的若干注记

Remarks on the Levi core

本文研究Levi核的基本有限性问题，并探讨其与Kohn算法及Catlin性质(P)的联系。

Sufficient condition for compactness of the $\overline{\partial}$-Neumann operator using the Levi core

On a smooth, bounded pseudoconvex domain $Ω$ in $\mathbb{C}^n$, to verify that Catlin's Property ($P$) holds for $bΩ$, it suffices to check that it holds on the set of D'Angelo infinite type boundary points. In this note, we consider the support of the Levi core, $S_{\mathfrak{C}(\mathcal{N})}$, a subset of the infinite type points, and show that Property ($P$) holds for $bΩ$ if and only if it holds for $S_{\mathfrak{C}(\mathcal{N})}$. Consequently, if Property ($P$) holds on $S_{\mathfrak{C}(\mathcal{N})}$, then the $\overline{\partial}$-Neumann operator $N_1$ is compact on $Ω$.

Homogeneous models for Levi-degenerate CR manifolds

We extend the notion of a fundamental negatively $\mathbb Z$-graded Lie algebra $\mathfrak{m}_x=\bigoplus_{p\leq -1}\mathfrak{m}_x^p$ associated to any point of a Levi nondegenerate CR manifold to the class of $k$-nondegenerate CR manifolds $(M,\mathcal D,\mathcal J)$ for all $k\geq 2$ and call this invariant the core at $x\in M$. It consists of a $\mathbb Z$-graded vector space $\mathfrak{m}_x=\bigoplus_{p\leq k-2}\mathfrak{m}_x^p$ of height $k-2$ endowed with the natural algebraic structure induced by the Tanaka and Freeman sequences of $(M,\mathcal D,\mathcal J)$ and the Levi forms of highe…

Levi $q$-核与性质 ($P_q$)

The Levi $q$-core and Property ($P_q$)

本文引入Grassmannian $q$-核，推广了核概念，并证明在伪凸域上其支撑满足性质$(P_q)$当且仅当边界满足该性质，推广了$q=1$的结果，为广义分层提供新视角。

Deformations of Levi flat hypersurfaces in complex manifolds

We first give a deformation theory of integrable distributions of codimension 1. We define a parametrization of families of smooth hypersurfaces near a Levi flat hypersurface L such that the Levi flat deformations are given by the solutions of the Maurer-Cartan equation in a DGLA associated to the Levi foliation. We say that L is infinitesimally rigid if the tangent cone at the origin to the moduli space of Levi flat deformations of L is trivial. We prove the infinitesimal rigidity of compact transversally parallelisable Levi flat hypersurfaces in compact complex manifolds and give sufficient …