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PreprintCC BY 4.0arXiv

A Converse to the Skoda L2 division theorem II

  • Zhi Li
  • Xiankui Meng
  • Jiafu Ning
  • Xiangyu Zhou
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Abstract

We prove a converse to the original Skoda L2 division theorem, asserting that Skoda L2 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 L2 extension theorem directly from the division estimates.

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Cite

BibTeXRIS
BibTeX
@misc{li2026converse,
  title = {{A Converse to the Skoda $L^2$ division theorem II}},
  author = {Zhi Li and Xiankui Meng and Jiafu Ning and Xiangyu Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.33300},
  eprint = {2609.33300},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.33300},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A Converse to the Skoda L^2 division theorem II
AU  - Zhi Li
AU  - Xiankui Meng
AU  - Jiafu Ning
AU  - Xiangyu Zhou
PY  - 2026
DA  - 2026/09/27
PB  - arXiv
DO  - 10.48550/arxiv.2609.33300
UR  - https://arxiv.org/abs/2609.33300
AB  - 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.
ER  -