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arXiv · 2609.07697

A two-dimensional counterexample for Kobayashi completeness of balanced domains

Armen Edigarian
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Abstract

Jarnicki and Pflug constructed a bounded balanced domain of holomorphy in $\mathbb C^n$, $n\ge 3$, 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 $\mathbb C^2$.

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Armen Edigarian. 2026-09-07. A two-dimensional counterexample for Kobayashi completeness of balanced domains. https://arxiv.org/abs/2609.07697

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