PreprintCC BY 4.0arXiv
CSC Bergman metrics are Einstein on pseudoconvex domains
Abstract
Let Ω⊂ℂn(n≥ 3) be a pseudoconvex domain with a smooth strongly pseudoconvex boundary point. We prove that if the Bergman metric of Ω has constant scalar curvature, then it is necessarily Kähler--Einstein.
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BibTeX
@misc{li2026bergman,
title = {{CSC Bergman metrics are Einstein on pseudoconvex domains}},
author = {Xiaoshan Li and Taishun Liu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24853},
eprint = {2609.24853},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24853},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - CSC Bergman metrics are Einstein on pseudoconvex domains
AU - Xiaoshan Li
AU - Taishun Liu
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24853
UR - https://arxiv.org/abs/2609.24853
AB - Let Ω⊂ℂ^n(n≥ 3) be a pseudoconvex domain with a smooth strongly pseudoconvex boundary point. We prove that if the Bergman metric of Ω has constant scalar curvature, then it is necessarily Kähler--Einstein.
ER -