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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2403.19553 |
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| _version_ | 1866918348368904192 |
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| author | Aoi, Takahiro |
| author_facet | Aoi, Takahiro |
| contents | In this paper, we prove the Skoda-Zeriahi type integrability theorem with respect to some measure with $L^1$-density. In addition, we introduce the log-log threshold in order to detect singularities of Kähler potentials. We prove the positivity of the integrability threshold for such a measure and Kähler potentials with uniform log-log threshold. As an application, we prove the entropy compactness theorem for a family of potential functions of Poincaré type Kähler metrics with uniform log-log threshold. The Ohsawa-Takegoshi $L^2$-extension theorem and Skoda-Zeriahi's integrability theorem play a very important role in this paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19553 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Skoda-Zeriahi type integrability and entropy compactness for some measure with $L^1$-density Aoi, Takahiro Differential Geometry Complex Variables 31U05 In this paper, we prove the Skoda-Zeriahi type integrability theorem with respect to some measure with $L^1$-density. In addition, we introduce the log-log threshold in order to detect singularities of Kähler potentials. We prove the positivity of the integrability threshold for such a measure and Kähler potentials with uniform log-log threshold. As an application, we prove the entropy compactness theorem for a family of potential functions of Poincaré type Kähler metrics with uniform log-log threshold. The Ohsawa-Takegoshi $L^2$-extension theorem and Skoda-Zeriahi's integrability theorem play a very important role in this paper. |
| title | Skoda-Zeriahi type integrability and entropy compactness for some measure with $L^1$-density |
| topic | Differential Geometry Complex Variables 31U05 |
| url | https://arxiv.org/abs/2403.19553 |