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PreprintarXiv licencearXiv

From the Optimal L2-Estimates (p,n) and (n,p)-Forms to Uniform Griffiths p-Positivity via Convolution and Restriction

  • Zhuo Liu
  • Xujun Zhang
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Abstract

We prove that the optimal L2-estimate property for (p,n)-forms is preserved under standard convolution regularization. As an application, we show that a singular Hermitian metric satisfying the optimal L2-estimate property for (p,n)-forms is uniform Griffiths p-positive. By establishing the restriction property, we prove that a singular Hermitian metric satisfying the optimal L2-estimate property for (n,p)-forms is also uniform Griffiths p-positive.

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Cite

BibTeXRIS
BibTeX
@misc{liu2026from,
  title = {{From the Optimal $L^2$-Estimates \((p,n)\) and \((n,p)\)-Forms to Uniform Griffiths \(p\)-Positivity via Convolution and Restriction}},
  author = {Zhuo Liu and Xujun Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.28236},
  eprint = {2610.28236},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.28236},
}
RIS
TY  - UNPB
TI  - From the Optimal L^2-Estimates (p,n) and (n,p)-Forms to Uniform Griffiths p-Positivity via Convolution and Restriction
AU  - Zhuo Liu
AU  - Xujun Zhang
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.28236
UR  - https://arxiv.org/abs/2610.28236
AB  - We prove that the optimal L^2-estimate property for (p,n)-forms is preserved under standard convolution regularization. As an application, we show that a singular Hermitian metric satisfying the optimal L^2-estimate property for (p,n)-forms is uniform Griffiths p-positive. By establishing the restriction property, we prove that a singular Hermitian metric satisfying the optimal L^2-estimate property for (n,p)-forms is also uniform Griffiths p-positive.
ER  -