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On compactness of the $\bar{\partial}$-Neumann operator on $r$-convex domains
Le Mau Hai
,
Nguyen Xuan Hong
Abstract
In this paper, we show that on a bounded $r$-convex domain $\Omega$ in $\mathbb C^n$ such that for every $z\in \partial\Omega$ there exists a complex affine subspace $L_z$ of dimension $\le q−1$ through $z$ such that $L_z \cap\partial\Omega$ is a $q$-peak set with $r\le q\le n$ the $\bar{\partial}$-Neumann operator $N_{q,\Omega}$ is compact.