Analytic discs and compactness of the ∂-Neumann operator
Qianyun Wang, Yuan Yuan, Xu Zhang
Abstract
We construct a bounded pseudoconvex complete Reinhardt domain Ω with smooth boundary in C3 such that the ∂-Neumann operator N1 is compact although bΩ contains an analytic disc and thus also fails Catlin's Property (P) and McNeal's Property ( P). This example solves an open problem on compactness of the ∂-Neumann operator in the negative.
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