Year: 2026
Type: preprint
Abstract: We construct a bounded pseudoconvex complete Reinhardt domain $Ω$ with smooth boundary in $\mathbb{C}^3$ such that the $\bar\partial$-Neumann operator $N_1$ is compact although $bΩ$ contains an analytic disc and thus also fails Catlin's Property $(P)$ and McNeal's Property $(\tilde P)$. This example solves an open problem on compactness of the $\bar\partial$-Neumann operator in the negative.
Source: arXiv (Cornell University)
Authors: Wang, Qianyun, Yuan, Yuan, Zhang, Xu
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7206170990