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Pseudoconvex domains in complex Euclidean space with finite-dimensional Bergman spaces

Year: 2026
Type: preprint
Abstract: We construct a pseudoconvex domain in $\mathbb{C}^2$ such that the Bergman space is one-dimensional. Based on this example, for any integers $n \geq 3, d \geq 1$, we further construct a pseudoconvex domain in $\mathbb{C}^n$ such that the Bergman space is $d$-dimensional. This disproves Wiegerinck's conjecture.
DOI: 10.48550/arxiv.2610.21749
Author: Yuan, Yuan
Language: English
Open Access status: green
OpenAlex ID: W7222468468
Cites: 3
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Related to: 10