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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2210.17361 |
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| _version_ | 1866916297954033664 |
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| author | Liu, Zhuo Xu, Wang |
| author_facet | Liu, Zhuo Xu, Wang |
| contents | Deng-Ning-Wang-Zhou showed that a Hermitian holomorphic vector bundle is Griffiths semi-positive if it satisfies the optimal $L^2$-extension condition. As a generalization, we present a quantitative characterization of Griffiths positivity in terms of certain $L^2$-extension conditions. We also show that a $\mathbb{R}$-valued measurable function is pluriharmonic if and only if it satisfies the equality part of the optimal $L^p$-extension condition. This answers a conjecture of Inayama affirmatively. Moreover, the flatness of a possibly singular Hermitian metric is also equivalent to the equality part of the optimal $L^p$-extension condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_17361 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Characterizations of Griffiths Positivity, Pluriharmonicity and Flatness Liu, Zhuo Xu, Wang Complex Variables Deng-Ning-Wang-Zhou showed that a Hermitian holomorphic vector bundle is Griffiths semi-positive if it satisfies the optimal $L^2$-extension condition. As a generalization, we present a quantitative characterization of Griffiths positivity in terms of certain $L^2$-extension conditions. We also show that a $\mathbb{R}$-valued measurable function is pluriharmonic if and only if it satisfies the equality part of the optimal $L^p$-extension condition. This answers a conjecture of Inayama affirmatively. Moreover, the flatness of a possibly singular Hermitian metric is also equivalent to the equality part of the optimal $L^p$-extension condition. |
| title | Characterizations of Griffiths Positivity, Pluriharmonicity and Flatness |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2210.17361 |