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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.19553 |
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Table of 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.