PreprintCC BY 4.0arXiv
A two-dimensional counterexample for Kobayashi completeness of balanced domains
Abstract
Jarnicki and Pflug constructed a bounded balanced domain of holomorphy in ℂn, n≥ 3, with continuous Minkowski function which is not Kobayashi complete, and explicitly asked whether the same phenomenon can occur in dimension two. We give such a domain in ℂ2.
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BibTeX
@misc{edigarian2026twodimensional,
title = {{A two-dimensional counterexample for Kobayashi completeness of balanced domains}},
author = {Armen Edigarian},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07697},
eprint = {2609.07697},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07697},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A two-dimensional counterexample for Kobayashi completeness of balanced domains
AU - Armen Edigarian
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.07697
UR - https://arxiv.org/abs/2609.07697
AB - Jarnicki and Pflug constructed a bounded balanced domain of holomorphy in ℂ^n, n≥ 3, with continuous Minkowski function which is not Kobayashi complete, and explicitly asked whether the same phenomenon can occur in dimension two. We give such a domain in ℂ^2.
ER -