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arXiv · 2506.22834

An Ohsawa-Takegoshi-type $L^2$ extension for upper semi-continuous $L^2$-optimal functions

Zhuo Liu
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Abstract

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.

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Zhuo Liu. 2025-06-28. An Ohsawa-Takegoshi-type $L^2$ extension for upper semi-continuous $L^2$-optimal functions. https://arxiv.org/abs/2506.22834

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