论文标题
使用Levi Core
Sufficient condition for compactness of the $\overline{\partial}$-Neumann operator using the Levi core
论文作者
论文摘要
在$ \ Mathbb {C}^n $中的平滑，有限的pseudoconvex域$ω$，以验证Catlin的属性（$ p $）以$bΩ$持有，足以检查其在D'Angelo Infinite类型边界点上是否保留。在本注中，我们考虑Levi Core的支持，$ s _ {\ Mathfrak {C}（\ Mathcal {n}）} $，无限类型点的子集，并显示该属性（$ p $）在$bΩ$中均为$ s _ _ _ {\ nathfrak} $ s _ {cc} $ n of $bΩ因此，如果属性（$ p $）在$ s _ {\ mathfrak {c}（\ mathcal {n}）} $上持有，则$ \ overline {\ partial} $ - neumann operator $ n_1 $是$ω$的compact。
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 $Ω$.
