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arXiv · 2403.19553

Skoda-Zeriahi type integrability and entropy compactness for some measure with $L^1$-density

Takahiro Aoi
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Abstract

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 K\"{a}hler potentials. We prove the positivity of the integrability threshold for such a measure and K\"{a}hler potentials with uniform log-log threshold. As an application, we prove the entropy compactness theorem for a family of potential functions of Poincar\'{e} type K\"{a}hler 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.

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Takahiro Aoi. 2024-03-28. Skoda-Zeriahi type integrability and entropy compactness for some measure with $L^1$-density. https://arxiv.org/abs/2403.19553

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