An Ohsawa-Takegoshi-type $L^2$ extension for upper semi-continuous $L^2$-optimal functions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913917055270912 |
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| author | Liu, Zhuo |
| author_facet | Liu, Zhuo |
| contents | In this article, we obtain an Ohsawa-Takegoshi-type $L^2$-extension for upper semi-continuous $L^2$-optimal functions via a Lebesgue-type differentiation theorem. As applications, we give a characterization of plurisubharmonic functions via the multiple coarse $L^2$-estimate property for (strongly) upper semi-continuous functions and show that (strongly) upper semi-continuous $L^2$-optimal functions satisfy Skoda's integrability theorem and the strong openness property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_22834 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Ohsawa-Takegoshi-type $L^2$ extension for upper semi-continuous $L^2$-optimal functions Liu, Zhuo Complex Variables 32U05, 32D15, 42B25, 14F18 In this article, we obtain an Ohsawa-Takegoshi-type $L^2$-extension for upper semi-continuous $L^2$-optimal functions via a Lebesgue-type differentiation theorem. As applications, we give a characterization of plurisubharmonic functions via the multiple coarse $L^2$-estimate property for (strongly) upper semi-continuous functions and show that (strongly) upper semi-continuous $L^2$-optimal functions satisfy Skoda's integrability theorem and the strong openness property. |
| title | An Ohsawa-Takegoshi-type $L^2$ extension for upper semi-continuous $L^2$-optimal functions |
| topic | Complex Variables 32U05, 32D15, 42B25, 14F18 |
| url | https://arxiv.org/abs/2506.22834 |