A Converse to the Skoda $L^2$ division theorem II

Zhi Li; Xiankui Meng; Jiafu Ning; Xiangyu Zhou

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arXiv · 2609.33300

A Converse to the Skoda $L^2$ division theorem II

Zhi Li·Xiankui Meng·Jiafu Ning·Xiangyu Zhou

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Abstract

We prove a converse to the original Skoda $L^2$ division theorem, asserting that Skoda $L^2$ division estimates for a single nonzero holomorphic function force the weight to be plurisubharmonic. In addition, we establish corresponding results for higher-rank quotient bundles. Finally, we derive an optimal $L^2$ extension theorem directly from the division estimates.

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Zhi Li, Xiankui Meng, Jiafu Ning, Xiangyu Zhou. 2026-09-27. A Converse to the Skoda $L^2$ division theorem II. https://arxiv.org/abs/2609.33300

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