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arXiv · 2610.21749

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

Yuan Yuan
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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.

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Yuan Yuan. 2026-10-17. Pseudoconvex domains in complex Euclidean space with finite-dimensional Bergman spaces. https://arxiv.org/abs/2610.21749

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