From the Optimal $L^2$-Estimates $(p,n)$ and $(n,p)$-Forms to Uniform Griffiths $p$-Positivity via Convolution and Restriction

Zhuo Liu; Xujun Zhang

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arXiv · 2610.28236

From the Optimal $L^2$-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 $L^2$-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.

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Zhuo Liu, Xujun Zhang. 2026-10-20. From the Optimal $L^2$-Estimates $(p,n)$ and $(n,p)$-Forms to Uniform Griffiths $p$-Positivity via Convolution and Restriction. https://arxiv.org/abs/2610.28236

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