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A new characterization of domains of holomorphy with $L^2$-optimal conditions

Zhuo LiuXujun Zhang
Feb 2024
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摘要原文
We show that the $L^2$-optimal condition indicates $L^2$-divisibility of $L^2$-integrable holomorphic functions and we show that any bounded $L^2$-optimal domain with null thin complement is an $L^2$-domain of holomorphy. As an application, we construct an $L^2$-optimal domain which does not admit any complete K\"ahler metric, which shows that the $L^2$-optimal condition is more flexible than the complete K\"ahler condition.
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