Qianyun Wang

Analytic discs and compactness of the $\bar\partial$-Neumann operator

We construct a bounded pseudoconvex complete Reinhardt domain $\Omega$ with smooth boundary in $\mathbb{C}^3$ such that the $\bar\partial$-Neumann operator $N_1$ is compact although $b\Omega$ contains an analytic disc and thus also fails Catlin's Property $(P)$ and McNeal's Property $(\tilde P)$. This example solves an...