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Pseudoconvex domains in complex Euclidean space with finite-dimensional Bergman spaces
Abstract
We construct a pseudoconvex domain in ℂ2 such that the Bergman space is one-dimensional. Based on this example, for any integers n ≥ 3, d ≥ 1, we further construct a pseudoconvex domain in ℂn such that the Bergman space is d-dimensional. This disproves Wiegerinck's conjecture.
Related
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- CSC Bergman metrics are Einstein on pseudoconvex domains
- Comparison of the Bergman and Szegő kernels on arbitrary bounded pseudoconvex domains with C2 boundary
- Rigidity of Extremal and cscK Bergman Metrics on Pseudoconvex Domains
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BibTeX
@misc{yuan2026pseudoconvex,
title = {{Pseudoconvex domains in complex Euclidean space with finite-dimensional Bergman spaces}},
author = {Yuan Yuan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21749},
eprint = {2610.21749},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21749},
}
RIS
TY - UNPB
TI - Pseudoconvex domains in complex Euclidean space with finite-dimensional Bergman spaces
AU - Yuan Yuan
PY - 2026
DA - 2026/10/17
PB - arXiv
DO - 10.48550/arxiv.2610.21749
UR - https://arxiv.org/abs/2610.21749
AB - We construct a pseudoconvex domain in ℂ^2 such that the Bergman space is one-dimensional. Based on this example, for any integers n ≥ 3, d ≥ 1, we further construct a pseudoconvex domain in ℂ^n such that the Bergman space is d-dimensional. This disproves Wiegerinck's conjecture.
ER -