A new characterization of $L^2$-domains of holomorphy with null thin complements via $L^2$-optimal conditions
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909206119972864 |
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| author | Liu, Zhuo Zhang, Xujun |
| author_facet | Liu, Zhuo Zhang, Xujun |
| contents | In this paper, we show that the $L^2$-optimal condition implies the $L^2$-divisibility of $L^2$-integrable holomorphic functions. As an application, we offer a new characterization of bounded $L^2$-domains of holomorphy with null thin complements using the $L^2$-optimal condition, which appears to be advantageous in addressing a problem proposed by Deng-Ning-Wang. Through this characterization, we show that a domain in a Stein manifold with a null thin complement, admitting an exhaustion of complete Kähler domains, remains Stein. By the way, we construct an $L^2$-optimal domain that does not admit any complete Kähler metric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_05082 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A new characterization of $L^2$-domains of holomorphy with null thin complements via $L^2$-optimal conditions Liu, Zhuo Zhang, Xujun Complex Variables 32W05, 32D05 In this paper, we show that the $L^2$-optimal condition implies the $L^2$-divisibility of $L^2$-integrable holomorphic functions. As an application, we offer a new characterization of bounded $L^2$-domains of holomorphy with null thin complements using the $L^2$-optimal condition, which appears to be advantageous in addressing a problem proposed by Deng-Ning-Wang. Through this characterization, we show that a domain in a Stein manifold with a null thin complement, admitting an exhaustion of complete Kähler domains, remains Stein. By the way, we construct an $L^2$-optimal domain that does not admit any complete Kähler metric. |
| title | A new characterization of $L^2$-domains of holomorphy with null thin complements via $L^2$-optimal conditions |
| topic | Complex Variables 32W05, 32D05 |
| url | https://arxiv.org/abs/2401.05082 |